34527173-Constrained-Motion-Question-Bank-02.pdf

8/14/2019 34527173-Constrained-Motion-Question-Bank-02.pdf

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Mohammed

Asif

Name :

Roll No. :

Topic :

Ph : 9391326657, 64606657

P!"#$" %&$%'

Ma(ch (he col)m* (+pe )es(io*s1. -o a pa(icle mo/i* alo* a cicle of adi)s , a( a i/e* i*s(a*( of (ime

'is( # 'is( ##

# $e*(ipe(al accelea(io* 0 implies (ha( A ac 0

## Ta*e*(ial accelea(io* 0, implies (ha( aT 0

### #f speed is i*ceasi* $ a*le e(ee* /eloci(+ a*d

a is o()se

# #f (he speed is deceasi* 8 a*le e(ee*

Ca a*d

a is ac)(e

A #A, ##, ###8, #$8 #A, ##$, ###8, #

$ #, ##$, ###A, #8 8 #8, ##A, ###, #$

2. A pa(icle is pefomi* cic)la mo(io*. The* if

'is( # 'is( ##

# #( has a co*s(a*( speed, (he* A #( ca*( follo a cic)la pa(h

## #( has a /a+i* speed, (he* #( ca* ha/e /a+i* ma*i()de of accelea(io*

### #( has /a+i* /eloci(+, (he* $ #( has co*s(a*( ma*i()de of accelea(io*

diec(ed (oads (he ce*(e.

# #( has a co*s(a*( /eloci(+, (he* 8#(s accelea(io* also has a (a*e*(ial compo*e*(A #A, ##8, ###$, #A #A, ##, ###8, #A

$ #8, ##$, ###A, # 8 #8, ##A, ###, #$

3. To pa(icles A a*d ae mo/i* i* 2co*ce*(ic cicles of adii Aa*d espec(i/el+ i* same

pla*e. The a*)la /eloci(+ of A is A a*d (ha( of is B . A( ( 0, o(h ae i* same phase,

(he* if

'is( # 'is( ##

# == BA a*d 2A , (he* ela(i/e A 2/5 a*)la /eloci(+ of ..(. A a( ( 0, is

## == BA 2 a*d A 2, (he* ela(i/e 2/

a*)la /eloci(+ of ..(. A a( ( 0, is

### == BA 3 a*d 3A , (he* ela(i/e $ ;eo a*)la /eloci(+ of ..(. A a( ( 0, is

# == 2/BA a*d A


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4. A pa(icle is mo/i* alo* a paaolic pa(h + >2. A( (he i*s(a*( he* (he pa(icle is a(

2

+


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6. A pa(icle is mo/i* i* cicle i* >+ pla*e of e)a(io* >2@ +2 1 i(h a* a*)la /eloci(+ '' ,

if

'is( # 'is( ##

# ( ) ( ) ( )0,cotcos 00 >= VVVy a*d (he pa(icle

co/es comple(e cicle i* 2/ sec, (he* A a(2

1,

2

1== yx

## ( ) ( )0,cotcos 00 += VtVVy a*d 2=t a( ( sec,4/=t (he* $ a( (ime xVsec,16/ ill e 0

# ( ) ( )0,4/cos 00 >+= VtVVy , if sec/4rad= 8 a( xVyx ,2

1,

2

1 == ill

e

2/0

V

A #A, ##8, ###$, # #A, ##, ###$, #8

$ #$, ##A, ###, #8 8 #, ##$, ###, #A8

7. A pa(icle is pefomi* cic)la mo(io* s)ch (ha( ( )0> . The acvs ta*d tsv / aphs fo(he mo(io* ae plo((ed i* lef( col)m*

'is( # 'is( ##

# A aTB 0

## aT 0

### $ pa(icle is speedi* )p

# 8 pa(icle is speedi* do*

www.asifiitphysics.vriti.com 3
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. A pa(icle is mo/i* alo* a cicle >2@ +2 a2i* hoi;o*(al pla*e i(h a*)la /eloci(+

2ad=sec. A ma* is mo/i* alo* (he > 2a i* @ diec(io* i(h /eloci(+ 4a m=s i* (he same

pla*e. A( ( 0, pa(icle a*d ma* ae alo* li*e + a

'is( # 'is( ##

# A( 2/=t , (he a*le made + (he li*e of mo(io* of

pa(icle i(h li*e paallel (o >a>is ..(. ma* is A ( 221ta 1 ++

## A( 8/=t (he a*le made + (he li*e of mo(io* of

pa(icle i(h li*e paallel (o >a>is ..(. ma* is aji

+

^^

422

### A( 4/3=t , (he /eloci(+ of pa(icle ..(. ma* is $ 2/

# A( , (he a*le made + (he li*e of mo(io* of pa(icle

i(h (he li*e paallel (o >a>is ..(. ma* is 8

^^

42 jaia +A #A, ##, ###$, #8 #, ##$, ###A, #A

$ #$, ##A, ###, #8 8 #A, ##8, ###$, #

9. A pa(icle mo/i* i* hoi;o*(al pla*e alo* a c)/e hose e)a(io* i* pola coodi*a(es iscos2ar=

'is( # 'is( ##

# #f ,60!/5/0== sraddtd (he* A ( ) 2/21

3

100sm

aaN +=

## #f 10a m=s a*d ,300

= (he* 2

/3

50

sm

a

aT=

### #f0

2

2

453

25 == anddt

d, (he* $

2/100 smaaN=

# #f ,2/sec/10 radandrad == (he* 82

/32

50sm

AaT

+=

%2

/0 smaT =

A #A, ##, ###$, #8 #$8, ##$, ###A, #$%

$ #$, ##A, ###, #8 8 #A, ##8, ###$, #

10. A massless i* is olli* o* fic(io*less s)face i(h /eloci(+ C a*d a*)la /eloci(+ ''

s)ch (ha(

'is( # 'is( ##

# Accelea(io* /ec(os of poi*(s A D ae A 8iec(ed (oads ce*(e



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## eloci(+ /ec(os of poi*(s A D ae pepe*dic)la (o each o(he.

### Accelea(io* /ec(os of poi*(s D $ ae $ a( a*le 450i(h each o(he.

# eloci(+ /ec(os of poi*(s D $ ae 8 i* opposi(e diec(io*s

A #$, ##$, ###$, #A #A, ##, ###$, #8

$ #A, ##$, ###A8, # 8 #A, ##8, ###$, #

Ei*ema(ics#

11. A d)*Fad ma* mo/es 5m eas( 10m *o(h a*d (he* 20m so)(hes(. -i*d o)( (he (o(al dis(a*cea*d displaceme*( (aced.

12. A heel is olli* o* hoi;o*(al s)face. -i*d o)( (he displaceme*( of a poi*( maF a( (he

o((om mos( poi*( o* heel of adi)s R hich olls half e/ol)(io*.

13. #* (he ao/e e>ample co*side (he poi*( o* (he e>(eme ih(. Ge( (he disp. fo half e/ol)(io*.

14. #* a cic)la mo(io*, plo( (he aph of displaceme*( vsa*le .

15. A (ai* mo/es a dis(a*ce s i(h speed /1a*d comes acF alo* same pa(h same dis(a*ce s i(h

speed /2. -i*d o)( a/eae speed a*d a/eae /eloci(+.

16. #f (he (ai* mo/es i(h speed /1fo fis( half (ime a*d speed /2fo seco*d half(ime. -i*d o)(

(he a/eae displaceme*(.

17. A pa(icle has i*i(ial /eloci(+ 10m=s eas(, accelea(io* 5m=s2is i/e* i* *o(h diec(io*. -i*d

o)( (he fi*al /eloci(+ a*d displaceme*( a( ( 2 sec a*d diec(io*.

1. A (ai* s(a(s fom es( i(h accelea(io* a, mo/es )*ifoml+ a*d (he* e(ads i(he(ada(io* , (he* comes (o es(. #f (o(al displaceme*( (a/elled is s, fi*d (he mi*im)m (ime

(aFe* (o co/e (he dis(a*ce.

19. A alloo* s(a(s isi* )p i(h a* accelea(io* a 5m=s2, a( ( 4 sec. (he s(o*e is dea((ached,

hich fis( ises )p a*d (he* comes do*. -i*d o)( (he (o(al (ime (aFe* of s(o*e efoe hi((i*

(he o)*d. Plo( (he displaceme*( /s. (ime aph.

20. $o*side (he disp. & as a f)*c(io* of (ime (. > 4( (2



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21. $o*side (he po(i(io* > as a f)*c(io* of (. >


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29. A alloo* s(a(s isi* fom (he ea(hs s)face. The accessio* a(e is co*s(a*( a*d e)al (o /0.

8)e (o (he i*d, (he alloo* a(hes (he hoi;o*(al /eloci(+ compo*e*( /> F+ hee F is a

co*s(a*( a*+ is a heih( of asce*(. -i*d ho (he folloi* )a*(i(ies depe*d o* (he heih( of

asce*(.

a The hoi;o*(al dif( of (he alloo* >


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3. A ()cF is mo/i* i(h a /eloci(+ 36Fm=h. H* seei* ed lih( i( decelea(es a( 2m=s. The efle>

(ime of (he di/e is 0.4sec. o m)ch dis(a*ce ill ()cF (a/el efoe comi* (o a s(opK

a 25 m 29 m c 35 m d No*e of (hese

39. A clocF has mi*)(e ha*d of 10cm le*(h. The a/eae /eloci(+ of (he (ip of mi*)(e ha*d fom

6am (o 6:30am is

a 2 = 3 cm=mi* 3/2 cm=mi* c 3/ cm=mi* d No*e of (hese

40. A i/e is 1Fm ide a*d flos a( a a(e 4Fm=h. A ma* is capale (o sim 3F=h. Lhee ill he

la*d if he s(iFes *omall+ (o (he flo of i/eK

a 1Fm I)s( opposi(e am km3

4aa+ c km

4

3aa+ d No*e of (hese

41. Rai* falli* /e(icall+ do*ads i(h a /eloci(+ of 3Fm=h. A peso* mo/es o* a s(aih( li*e

oad i(h a /eloci(+ of 4Fm=h. The* (he appae*( /eloci(+ of (he ai* ..(. (he peso* is

a 1 Fm=h 5 Fm=h c 4 Fm=h d 3 Fm=h

HIec(i/e )es(io*s i(h moe (ha* o*e coec( choices42. To cas A a*d s(a( fom es( a*d mo/e (oe(he fo (he same (ime i*(e/al. Thei

accelea(io* aphs ae as follos:

a o(h (he cas a((ai* (he same /eloci(+ af(e 10sec.

The /eloci(+ of ca is moe (ha* (ha( of A af(e 10sec.

c The dis(a*ce (a/elled + (he ca is moe (ha* (ha( of A af(e 10sec.d o(h (he cas (a/el (he same dis(a*ce af(e 10 sec.

43. A pa(icle mo/es 10m i* (he fis( 2sec, 20m i* (he *e>( 3sec a*d 30m i* (he *e>( (o 10sec. Lhich

of (he folloi* s(a(eme*(


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Radial /eloci(+dt

dr

t

PM

t

OPOM==

00"im"im Ta*e*(ial /eloci(+

dt

dr

t

r

t

QM

==

si"im"im

00

44. A pa(icle mo/es alo* a pa(h defi*ed + pola coodi*a(es 2e(a*d 28t= ad, i(s (a*e*(ial/eloci(+ a( ( 1 sec is

a 7 m=s. 174 m=s c 43 m=s d 54 m=s

45. #(s adial /eloci(+ a( ( 1sec is

a .7 m=s 7 m=s c 5.4 m=s d 54 m=s

8iec(io*s. J: 36 3: #* ma(hema(ic, (he s+mol . is )sed fo ea(es( i*(ee hich (he ma>.

possile /al)e i* i*(ee fo (ha( eal *)me e.., 4.3 4 a*d 6.3 7. $o*side a f)*c(io*

of acc. as (ime a (1, if (he od+ s(a(s fom es( ( 0

46. -i*d o)( (he /eloci(+ a( ( 3sec.

a 3 m=s 2 m=s c 1 m=s d 0 m=s

47. -i*d o)( (he disp. a( ( 3 sec

a 4 m 2 m c 0 m d 2 m

4. 8)i* (he mo(io* (he od+ has e/esed i(s diec(io* of mo(io* a(

a ( 1sec. ( 2 sec c ( 3 sec d ( 1.5 sec

Ma(ch (he folloi*:

49. 'is( # 'is( ##

# Ta*e*(ial acc. is ;eo A Rec(ili*ea )*ifom mo(io*

## H*l+ *omal acc. is ;eo O*ifom cic)la mo(io*

### Res)l(a*( acc. is ;eo $ No*)*ifom cic)la mo(io*.

# No*e of (he acc. is ;eo 8 O*ifoml+ accelea(ed moi(o*.

a #, ##8, ###$, #A #, ##8, ###A, #$c #8, ##$, ###A, # d #A, ##, ###$, #8

50. $o*side (he folloi* aphs, hee a acc., / /el., s disp.

'is( # 'is( ##

# A Possile

## Possile

### $ #mpossile



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# 8 #mpossile

a #$, ##, ###A, #8 #, ##$, ###8, #A

c #$, ##8, ###, #A d #A, ##8, ###, #$

N)meical J)es(io*s

51. To s(eel alls fall feel+ o* a* elas(ic sla. The fis( all is dopped fom a heih( h1a*d (he

seco*d fom a heih( h2


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57. $hecF (he ala*ce of eam.

5. -i*d o)( (he fee - applied + s)ppo( a*d a*le fo e)ilii)m.

59. #f a spi* ed i* a /e(ical pla*e. H*e e*d of a massless

spi* of *a()al le*(h 3R=4 is a((ached (o (he loes( poi*( H of (he ie (acF. A small i* ofmass m hich ca* slide o* (he (acF is a((ached (o (he o(he e*d of spi* maFes a* a*le 600

i(h (he /e(ical. The spi* co*s(a*(, F m=R. $o*side (he i*s(a*( he* (he i* is eleased.

a 8a -..8 of i* -i*d o)( (a*e*(ial acc. of i* a*d *omal eac(io* o* i(

61. -i*d o)( acc. of locFs a*d foce e>e(ed + clamp.


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63. -i*d o)( (he heih( h of i*cli*ed pla*e if a locF placed a( (op (aFes mi*im)m (ime (o slide

do*. ase le*(h is co*s(a*(.

64. To pa(icles each of mass m ae co**ec(ed + a lih( s(i* of le*(h 2' as sho*. Aco*(i*)o)s foce - is applied a( (he midpoi*( of (he spi* 0 a( ih( a*les (o (he i*i(ial

posi(io* of (he s(i*. "ho (ha( acc. of m i* (he diec(io* a( ih( a*le (o - i/e* +

222 xL

x

m

Fax

= .

65. ")ppose a lif( accelea(i* )p i(h accelea(io* a. -i*d o)( (he acc. of each locF ..(. lif(a*d (e*sio* i* (he s(i*.

M$Js i(h o*e coec( a*se

66. A )*ifom chai* of le*(h ' a*d mass m lies o* a smoo(h hoi;o*(al (ale i(h i(s le*(h

pepe*dic)la (o (he ede of (he (ale a*d small pa( o/eha*i*. The chai* s(a(s slidi*

do* fom es( d)e (o (he eih( of ha*i* pa(. -i*d (he accelea(io* a*d /eloci(+ of (he

chai* he* le*(h of (he ha*i* po(io* is >.

aL

xg

L

xg 2, xg

L

xg, c gL

L

xg, d ( )xLg

L

xg,

67. #f is coefficie*( of fic(io* e(ee* (he (+es a*d oad, (he* (he mi*im)m s(oppi* dis(a*cefo a ca of mass m mo/i* i(h /eloci(+ vis



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a gv g

v

2

2

c g2 d

g

v

2

6. Aalloo* of mass M is )*de a da foce - a*d )p(h)s( T. #( is mo/i* do* i(h a )*ifom

/eloci(+ v. Lha( amo)*( of mass e emo/ed so (ha( i( s(a(s isi* )p i(h same /eloci(+ vK

a M T= 2T = c T = d 2a>is

M

N cosalo* @/e >a>is

cM

N sialo* /e >a>is d

Mm

N

+

sialo* /e >a>is

70. #* (he ao/e polem *omal eac(io* e(ee* o)*d a*d ede ill ha/e ma*i()de e)al (o

a mgN +cos mgMgN ++cos c MgN +cos d mgMgN ++si

71. A pe*d)l)m of mass ha*s fom a s)ppo( fi>ed (o a (olle+. The diec(io* of (he s(i* he*

(he (olle+ olls )p a pla*e of i*cli*a(io* i(h accelea(io*, a, is

a ;eo (a*1 c

+

cos

sita

1

g

gad (a*1

g

a

72. To masses m a*d M ae a((ached i(h s(i*s as sho*. -o (he s+s(em (o e i* e)ilii)m,

e ha/e

am

M21ta +=

M

m21ta += c

m

M

21ta += d

m

M21ta +=



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73. All s)faces sho* i* (he fi)e ae smoo(h. "+s(em is eleased i(h (he spi* )*s(e(ched. #*

e)ilii)m, compessio* i* (he spi* ill e

ak

mg2

kmg2 c ( )

kgmM

2+ d k

mg

74. A sphee of mass m is held e(ee* (o smoo(h i*cli*ed alls. -o si*370 3=5, (he *omal

eac(io* of (he all e(ed + (he ope o* (he celli* is

a Ma @ m M


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7. A( (he i*s(a*( ( 0 a foce - F( e(ed + $ a*d 8 is 2P=5

d The accelea(io* of (he c)e 8 is P="m

Ma(ch T+pe J)es(io*s

2. Ma(ch (he acc. of locF m i* each ease. 'is( # 'is( ##

# A a



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##

### $ = 3

# 8 a 0

a #A, ##, ###$, #8 #A, ##$, ###, #A

c #, ##$, ###8, #A d #8, ##, ###A, #$

$ompehe*sio* J)es(io*s Passae 1:

To p)lle+s ae aa*ed as sho* i* fi. . foce )p (o 35 N, (he* ma>. (ime (he s+s(em

ill s)s(ai* is

a 70 sec. 140 sec. c 700 sec. d 35 sec.



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N)meical Polems

. -i. shos a locF of mass m a((ached (o a spi* of foce co*s(a*( F a*d co**ec(ed (o o)*d

+ (o s(i*s maFi* a* a*le 900i(h each o(he. #* ela>ed s(a(e *a()al le*(h is l. #* (he

si()a(io* sho* i* fi. fi*d (he (e*sio* i* (he (o s(i*s.

9. -i. shos a locF A o* a smoo(h s)face a((ached i(h a spi* of foce co*s(a*( F (o (he

ceili*. #* (his s(a(e spi* is i* *a()al le*(h l. The locF A is co**ec(ed + a massless a*d

fic(io* less s(i* (o a*o(he ide*(ical mass ha*i* o/e a lih( a*d smoo(h p)lle+. -i*d (he

dis(a*ce mo/ed + A efoe i( lea/es co*(ac( i(h (he o)*d.

Asse(io* D Reaso* T+pe J)es(io*s

8iec(io*s. J: 26 : The folloi* )es(io*s co*sis( of (o s(a(eme*(s. H*e laeled as Asse(io* a*d

o(he as Reaso*. $o*side (hese s(a(eme*(s a*d a*se.

a #f o(h Asse(io* a*d Reaso* ae ()e a*d Reaso* is coec( e>pla*a(io* of Asse(io*

#f o(h Asse(io* a*d Reaso* ae ()e )( Reaso* is *o( coec( e>pla*a(io* of Asse(io*

c #f Asse(io* is ()e )( Reaso* is false. d #f o(h Asse(io* a*d Reaso* ae false90. Asse(io*: -oces of ac(io* a*d eac(io* do *o( ca*cel each o(he. %ach pod)ces i(s o* effec(s

Reaso*: -oces of ac(io* a*d eac(io* ae e)al a*d opposi(e.

a c d

91. Asse(io*: A od+ )*de (he i*fl)e*ce of co*c)e*( foces i* e)ilii)m ei(he emai*s a( es(

o mo/es i(h a co*s(a*( /eloci(+.

Reaso*: $o*c)e*( foces ae said (o e i* e)ilii)m he* (he ma*i()de of (he es)l(a*(

foce is ;eo.

a c d

92. Asse(io*: A locF of mass M is s)spe*ded + a lih( cod $ a*d a s(o*e cod 8 is a((ached(o (he loe e*d. A s)dde* IeF is i/e* (o 8, (he* locF emai*s a( i(s place.

Reaso* : Te*sio* i* chod $ is less (ha* (ha( i* 8

a c d



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93. Asse(io*: To odies of mass 50 a*d 20 ae alloed (o fall fom (he same heih(. #f ai

esis(a*ce fo each is same, (he* o(h (he odies each (he ea(h sim)l(a*eo)sl+.

Reaso* : Accelea(io* of o(h (he odies is same.

a c d

94. Asse(io*: A id is si((i* o* (he floo of a ie cae a*d (he cae is i* (he ha*d of a o+. %/e*

he* (he id s(a(s fl+i* i* (he cae, (he o+ does *o( e>peie*ce a*+ cha*e i* (he eih( of(he cae

Reaso* : id is s(ill i* (he cae eca)se of hich (he o+ does *o( e>peie*ce a*+ cha*e.

a c d

N%LTHN" 'AL"

95. #* each of (he folloi* aa*eme*(s, fi*d


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a c d

e f h

97. #* each of (he folloi* aa*eme*(s, fi*d (he accelea(io* of each locF a*d (e*sio* i* (he

(head=s I)s( af(e (he locFs ae eleased fom es(. $o*side a/i(+

a

9. To small pa(icles ae es(ic(ed (o mo/e alo* (he edes of a smoo(h ie c)e as sho* i*

(he fi)e. The+ ae also co**ec(ed + a* ideal (head. #f (he mass of each pa(icle is M, fi*d (he

accelea(io* of each pa(icle I)s( af(e (he s+s(em is eleased fom es(. H*e of (he s+s(em is

eleased fom es(. H*e of (he sides co*(ai*i* pa(icle is hoi;o*(al a*d o(he is /e(ical.

99. #* each of (he folloi* cases, some pa(icles ae mo/i* alo* a ope as sho* i* (he fi)es.

-i*d (he (e*sio* i* all (he sec(io*s of (he ope i* each case. Nelec( a/i(+ i* pa(s a, e, f. All

accelea(io* ae i/e* ..( (he (head.

a c d

e f



20/51

100. #* (he folloi* (head=p)lle+ s+s(ems, calc)la(e (he accelea(io* of each mass a*d (e*sio* i*

each (head. Ass)me (ha( all (he (heads a*d p)llies ae ideal a*d (ha( (he s+s(ems ae eleased

fom es(.

a c d

e f

h

i I

101. #* each of (he folloi* cases, fi*d (he *e( foce applied + (he (heads o* each of (he clamps.

a c



21/51

RHTAT#HNA' MHT#HN


22/51

a2

3mvr

2

mvrc mvr d

3

2mvr

10. To poi*( masses of mass m a*d speed / s(icF (o a* e)ila(eal (ia*le made + (hee massless

ods a( (he e*d a*d $. The s+s(em is placed a( smoo(h pla*e a*d masses s(icF sim)l(a*eo)sl+

mo/i* *omal (o sides. The a*)la /eloci(+ af(e (he collisio* ill e

a2

3v

3

2vc

3

vd v2

109. A lih( c+li*de placed o* a s)face i(h coefficie*( fic(io* 5.0= is a((ached i(h a (hi* od

of mass m is eleased fom es( as sho* i* -i. -i*d (he accelea(io* of ce*(e of od af(e (he

elease

a2

g c 0 d g2

110. A sphee of mass M a*d adi)s + pla*e alo* (he

li*e + @ 4. The ma*i()de of (he a*)la mome*()m


23/51

113. A (hi* )*ifom ' shape od of mass 4F is hi*ed as sho*. Lhe* (he (head is c)( fi*d (he

i*i(ial accelea(io* of poi*( A.

a22

3g

5

23gc

2

3gd

3

2g

Moe (ha* o*e op(io*s ma+ e coec(

114. A (hi* od of le*(h 6m D mass 6m is i/e* a shap imp)lse of 120 Nsec a( poi*( 2m fom a*

e*d accodi* (o fi. The od is placed o* a smoo(h hoi;o*(al pla*e. Q)s( d)i* imp)lse od

eaFs )p i* (o pa(s a( (he poi*( of imp)lse. Ass)mi* imp)lse (o e di/ided e)all+ i* o(h

pa(s (he ela(i/e a*)la /eloci(+ of pa(s ill e

asec

30rad

sec

150 rad

csec

120 rad

d No*e of (hese

115. To simila pa(icles A a*d o(a(e i* >+ pla*e of adi)s Aa*d +; pla*e of adi)s ao)*d

/e(ical a>is passi* (ho)h (he ce*(e of (hei oi(s. The )*ifom a*)la /eloci(+ of A is

A a*d (ha( of is B , (he* ela(i/e a*)la accelea(io* a*d a*)la /eloci(+ ae

a AB 22

2

1,

4 BA

AB

+ c 22BA

+ d 222BABA

+

116. To peso*s of e)al mass m ae slidi* feel+ o* ice, each i(h a speed / o* paallel s(aih(

pa(h i* opposi(e diec(io*s. The pa(hs ae sepaa(ed + a pepe*dic)la dis(a*ce d. (he fis(

peso* caies a pole of le*(h lheld fiml+ a( o*e e*d. The seco*d peso* ips (he o(he e*d of

(he pole I)s( as (he+ ae passi* each o(he. Lhich of (he folloi* s(a(eme*(s ae ()e fo (he

s)se)e*( mo(io* i* a cic)la pa(hKa %ach peso* mo/es i* a cic)la pa(h of adi)s l

2

1i(h co*s(a*( speed /.

%ach peso*s mo/es i* a cic)la pa(h of adi)s2

lao)( a ce*(e hich i(self mo/es i(h

speed v.

c The (e*sio* i* (he pole emai*s co*s(a*(

d The+ come (o es( he* (he pole has o(a(ed (ho)h2

(o lie alo* (he diec(io* of oii*al



24/51

mo(io*.

117. The (o)e o* a od+ ao)( a i/e* poi*( is fo)*d (o e e)al (o A > ' hee A is a co*s(a*(

/ec(o a*d ' is a*)la mome*()m of (he od+ ao)( (ha( poi*( fom (his. #( follos (ha(

atd

ldis pepe*dic)la (o ' a( all i*s(a*( of (ime.

The compo*e*( of ' i* (he diec(io* of A does *o( cha*e i(h (ime.

c The ma*i()de of ' does *o( cha*e i(h (imed ' does *o( cha*e i(h (ime

11. A all olls do* a* i*cli*ed pla*e a*d ac)ies a /eloci(+ /, he* i( eaches (he o((om of (he

pla*e. #f (he same all slides i(ho)( fic(io* o* o(he pla*e a*d ac)ies olli* fom (he same

heih( do* a* e)all+ i*cli*ed smoo(h pla*e a*d ac)ies a /eloci(+ / s, hich of (he folloi*

s(a(eme*(s is=ae coec(K

a /B /seca)se a oF is do*e + (he olli* all aai*s( (he fic(io*al foce.

/? /seca)se (he a*)la /eloci(+ ac)ied maFes (he olli* all (o (a/el fas(e.

c / /s eca)se Fi*e(ic e*e+ of (o alls is same a( o((om of pla*e.

d /B /s, eca)se (he olli* all ac)ies o(a(io*al as ell as (a*sla(io*al Fi*e(ic e*e+.

119. To simila (hi* ods of mass m each maFi* a* a*le of 1200ae hi*ed a( poi*( P is i(h a*)la /eloci(+ of 4

ad=s a*d (he* caef)ll+ placed i(h i(s fla( face o* a hoi;o*(al s)face. The coefficie*( of

fic(io* is 3/1= . TaFe 10m=s2. The*

a (he a*)la e(ada(io* pod)ced ill e


25/51

a sec(io* A$ has ea(e Fi*e(ic e*e+ (ha* sec(io* A8$.

sec(io* $ has ea(e e*e+ (ha* sec(io* $8

c sec(io* $ has (he same Fi*e(ic e*e+ as sec(io* 8A.

d (he sec(io* A, $, $8 a*d 8A ha/e (he same Fi*e(ic e*e+

$ompehe*sio* A

-oce of fic(io* pla+s a ole of ()*i* foce i* mo(io* of a olli* iid od+. The foce of

fic(io* ala+s (ies (o oppose (he ela(i/e mo(io* e(ee* (he (o s)faces i* co*(ac(. As afoce i( ca* pod)ce li*ea accelea(io* as ell

122. A solid sphee o(a(i* i(h a* a*)la speed is p)( o* a lo* pla*F of mass e)al (o sphee.The fic(io* e>is(s e(ee* pla*F a*d sphee hile pla*F es(s o* a pla*e fic(io*less s)face,

(he*

a speed of ce*(e of sphee ill i*cease fis( (he* decease.

speed of ce*(e of sphee ill i*cease (he* ecome co*s(a*(.

c (he pla*F ill ha/e same accelea(io* as sphee ill ha/e.

d speed of ce*(e of mass of (he s+s(em ill e half of (ha( of speed of ce*(e of sphee.

123. $hoose (he coec( op(io*s


26/51

127. Mecha*ical e*e+ loss ill e ma>im)m fo (he /al)e of e)als (o

a3

1

4

1c

6

1d

12

1

12. 'oss of mecha*ical e*e+ i* ao/e case i* ".#. )*i(s is

a 210m 2100m c2

100md

2

10m

$ompehe*sio* $

T)*i* effec( of a foce is i/e* + (o)e, hee Fr= . A foce ma+ pod)ce ()*i* asell as li*ea effec(. $o*side a solid sphee of mass m a*d adi)s i* space hee (hee is *o

a/i(+ o a*+ o(he foce, a foce - is applied (a*e*(iall+ (o (he sphee + some mea* (he

diec(io* of foce does *o( cha*e + (ime.

129. The solid sphee ill mo/e i* a

a s(aih( li*e cic)la pa(h c (ooide pa(h d paaolic pa(h

130. The solid sphee ill ha/e

a li*ea accelea(e o*l+ a*)la accelea(io* o*l+ c ill ha/e o(h d No*e of (hese

131. $hoose (he coec( op(io*

a 'i*ea accelea(io*m

F= A*)la accelea(io*

mr

F

2

5=

c o(h of (hese d No a*)la accelea(io*

132. The sphee ill ha/e Fi*e(ic e*e+ i* (ime

am

tF

2

22

m

tF22

8

7c

m

tF22

4

7 d

m

tF

4

22

")Iec(i/e J)es(io*s

133. A (hi* )*ifom od A of mass m 1.0F mo/es (a*sla(io*all+ i(h accelea(io*2/0.2 sm=

d)e (o (o a*(ipaallel foce -1a*d -2


27/51

134. A sphee, a disc a*d a i* of (he same mass a*d adi)s ae olled fom es( fom (he (op of a

fic(io*less i*cli*ed pla*e sim)l(a*eo)sl+. #* hich ode do (he+ each (he o((om of (he

i*cli*eK

135. A )*ifom ladde of mass 20F a*d le*(h 4m es(s aai*s( a smoo(h all hee fic(io*

coefficie*( i(h o)*d e 5.0= . #f 10m=sec2, ha( ma>im)m a*le ladde co)ld maFe

i(h /e(ical meas)e a*le i* deeesK

136. A )*ifom od of mass 5.0F a*d le*(h l 90cm, es(s o* a smoo(h hoi;o*(al s)face, o*e of

(he e*d of (he od is s()cF i(h (he imp)lse Q 3.0 Ns i* hoi;o*(al diec(io* pepe*dic)la (o

(he od. As a es)l(, (he od o(ai*s (he mome*()m p 3.0 Ns. -i*d (he E.%. i(h hich od

ill mo/e.

Ma(chi* T+pe J)es(io*s

137. 'is( # 'is( ##

-o a od+ olli* do* o* a i*cli*ed ee (1B (2B (3B (4mass a*d adi)s ae

pla*e i(h o)( slippi*, (he (ime (aFe* same fo all odies

(o each o((om ill e

# Ri* A (3## "olid sphee (2### "olid c+li*de $ (4# ollo sphee 8 (1a #8, ##$, ###, #8 #$, ##8, ###, #A

c #8, ##, ###8, #$ d #8, ##, ###A, #$

13. 'is( # 'is( ##

# To)e A > p

## A*)la Mome*()m

2

L

### Poe $ > -

# %*e+ 8

a #$, ##A, ###, #8 #A, ##$, ###8, #

c #$, ##A, ###8, # d #A, ##$, ###, #8

139. 'is( # 'is( ##

# A M# ill e

mr2

3

##

( )222

14

RRM +

### $

( )22

2

1 5

4RR

M +



28/51

# 8

( )222

12

RRM +

a #, ##8, ###$, #A #, ##$, ###8, #A

c #8, ##A, ###, #$ d #$, ##, ###8, #A

140. 'is( # 'is( ##

# To)e a*)la accelea(io*, a*)la A Te*so

mome*()m, a*)la /eloci(+

## Mome*()m of i*e(ia Radial /ec(os

### A*)la displaceme*( of fi*i(e /al)e,

o(a(io*al Fi*e(ic e*e+ $ A>ial /ec(o

# $e*(ipe(al accelea(io*, ce*(ipe(al foce 8 No( /ec(os

a #$, ##A, ###8, # #, ##8, ###A, #$

c #A, ##$, ###, #8 d #, ##A, ###8, #$

141. A locF of mass 0.1F is held aai*s( a all + appl+i* a hoi;o*(al foce of 5N o* (he locF. #f

(he coefficie*( of fic(io* e(ee* (he locF a*d all is 0.5, (he ma*i()de of fic(io*al foce

ac(i* o* (he locF is

a 2.5 N 0.9 N c 4.9 N d 0.49 N

142. A locF of mass 2F es(s o* a pla*e i*cli*ed a( a* a*le of 300i(h (he hoi;o*(al. The

coefficie*( of fic(io* e(ee* (he locF a*d s)face is 0.7. Lha( is (he fic(io*al foce ac(i* o*

(he locFK

a 11.9 N 9.2 N c 15.75 N d 5. N

143. A 5F s(a(io*a+ om is e>ploded i* (hee pa(s ha/i* mass 1 : 1 : 3 espec(i/el+. Pa(s

ha/i* same mass mo/e i* pepe*dic)la diec(io* i(h /eloci(+ 39 m=s, (he* (he /eloci(+ of

ie pa( is

a sm /2

13 sm /210 c sm /

2

10d sm /213

144. A ship of mass 3 > 107F i*i(iall+ a( es( is p)lled + a foce of 5 > 104 N (ho)h a dis(a*ce of

3m. Ass)mi* (ha( (he esis(a*ce d)e (o a(e is *eliile, ha( ill e (he speed of shipK

a 0.1 m=s 1.5 m=s c 5 m=s d 0.2 m=s

145. To masses of 10F a*d 20F espec(i/el+ ae (ied (oe(he + a massless spi*. A foce of

200N is applied o* a 20F mass. A( (he i*s(a*( sho*, (he accelea(io* of 10F mass is 12m=s2,

(he accelea(io* of 20F mass is

a 0 m=s 10 m=s2 c 4 m=s2 d 12 m=s2



29/51

146. A oad of mass 5F is s)spe*ded fom a hoi;o*(al eam + (o s)ppo(i* ies, each a( a*

a*le of 450(o (he /e(ical. The (e*sio* of each ie is e(s a foce o* (he ocFe( e)al (o

a 60 N 600 N c 6000 N d 60000 N

149. A locF of mass M 15F ha*s + a cod fom a F*o( E of mass mFhich ha*s fom a

ceili* + mea*s of (o o(he cods. The cods ha/e *eliile mass, a*d (he ma*i()de o(he

a/i(a(io*al foce of (he F*o( is *eliile compaed (o (he a/i(a(io*al foce. The (e*sio*s i*

(he (hee cods ae

a NTNTNT 104,134,147 321 === NTNTNT 147,134,104 321 ===

c NTNTNT 147,104,134 321 === d NTNTT 147,134,,0 321 ===

150. Thee ae (o foce o* (he 2.0F o>. H*l+ o*e foce is sho*. The fi)e also shos (he

accelea(io* of (he o>. The ma*i()de of seco*d foce alo* i(h diec(io* is

a 3 N, 2130 20 N, 2130 c 42 N, 100 d 5 N, 100

151. A* 11F salami is s)ppo(ed + accod (ha( )*s (o a spi* scale, hich is s)ppo(ed +

a*o(he cod fom (he ceili*


30/51


31/51

a 2.1 m=s2 21 m=s2 c 5.1 m=s2 d 11 m=s2

157. A chai* co*sis(i* of fi/e li*Fs, each of m 0.100F is lif(ed /e(icall+ i(h a co*s(a*(accelea(io* of 2.50 m=s2. The ma*i()de of (he foce o* li*F 3 fom li*F 4 is

a 2.46 N 0.25 N c 3.69 N d 4.92 N

15. #f a cas heels ae locFed


32/51

a 0.5 0.33 c 0.19 d 0.23

161. A 1.34F sphee is co**ec(ed + mea*s of (o massless s(i*s, (o a /e(ical, o(a(i* od. The

s(i*s ae (ied (o (he od a*d ae (a)(. The (e*sio* i* (he )ppe s(i* is 35 N. The (e*sio* i*

(he loe s(i* is

a .74 N 6.45 N c 9.9 N d 7.4 N

162. A 1000 F oa( is (a/eli* a( 90 Fm=h he* i(s e*i*e is sh)( off. The ma*i()de of (he

fic(io*al focea

kf e(ee* oa( a*d a(e is popo(io*al (o (he speed of (he oa(.( )vfk 70=

hee vis i* me(es pe seco*d a*d kf i* Ne(o*s. The (ime e)ied + (he oa( (o slo (o

45 Fm=h isa 1 s 5 s c 12. s d 9.9 s

163. The mass of a* ele/a(o


33/51

166. A locF A of mass 7F placed o* a fic(io*less (ale. A (head (ied (o i( passes o/e a fic(io*less

p)lle+ a*d caies a od+ of mass 3F a( (he o(he e*d. The accelea(io* of (he s+s(em is


34/51

171. A* aeopla*e of mass 10,000 F e)ies a speed of 20ms1, fo (aFe off (he )* o* (he o)*d

ei* 100m. The coefficie*( of Fi*e(ic fic(io* e(ee* (he heels of (he pla*e a*d o)*d is

0.3. Ass)me (ha( pla*e accelea(es )*ifoml+ d)i* (aFe off. The mi*im)m foce e)ied +

(he e*i*e (o (aFe off

a 2 > 104 N 5 > 104 N c 3 > 104 N d 4 > 104 N

172. A ca(epilla cals )p a fi>ed hemispheical ol of adi)s R. #f (he coefficie*( of fic(io* is

31 . -i*d (he heih( as pece*(ae of adi)s )p(o hich ca(epilla ca* cal.

a 3 of R 5 of R c 7 of R d 9 of R

RHTAT#HNA' 8!NAM#$"##


35/51


36/51

a #f m1 24 F, fi*d m2s)ch (ha( (he s+s(em is i* e)ilii)m

#f 12 F is e*(l+ added (o (he (op of m1, fi*d (he a*)la accelea(io* of (he heels a*d (he

(e*sio* i* (he opes.

RHTAT#HNA' 8!NAM#$"##


37/51

14. A od A of le*(h ' a*d mass m is l+i* hoi;o*(all+ o* a hoi;o*(al fic(io*less (ale. The

od is pi/o(ed ao)( (he e*d A. ")ppose (ha( a hoi;o*(al foce of ma*i()de - is applied o*

e*d , s)ch (ha( is ala+s pepe*dic)la (o (he le*(h of (he od. Q)s( af(e (he foce is applied,

fi*d:

a a*)la accelea(io* of (he od. a*)la speed of (he od

c accelea(io* of ce*(e of mass of (he od. d foce ei* applied + (he od o* (he pi/o(

e foce of i*(eac(io* e(ee* a small pa(icle of mass dm a( (he midpoi*( of (he od a*d es( of(he od. f foce applied + o*e half of (he od o* (he o(he.

15. Thee pa(icles A, a*d $, each of mass m, ae co**ec(ed (o each o(he + (hee massless iid

ods (o fom a iid, e)ila(eal (ia*)la od+ of side l. This od+ is placed o* a hoi;o*(al

fic(io*less (ale + pla*e a*d is hi*ed (o i( a( (he poi*( A so (ha( i( ca* mo/e i(ho)(

fic(io* ao)( (he /e(ical a>is (ho)h A e(ed + (he hi*e o* (he od+

A( (ime T he* (he side $ is paallel (o (he >a>is, a foce - is applied o* alo* $

compo*e*( a*d (he +compo*e*( of (he foce e>e(ed + (he hi*e

o* (he od+, immedia(el+ af(e (ime T.

16. A )*ifom od A of mass m 2F a*d le*(h l 100cm is placed o* a shap s)ppo( H s)ch

(ha( AH a 40cm a*d H 60cm. A spi* of foce co*s(a*( E 600 Nm

1

is a((ached (oe*d as sho* i* (he fi)e. To Feep (he od hoi;o*(al, i(s e*d A is (ied i(h a (head s)ch

(ha( (he spi* is elo*a(ed + + 1cm. $alc)la(e eac(io* of s)ppo( H o* (he od he* (he

(head is )*( pess +o) a*se i* (ems of^

ia*d

^

j .



38/51

RHTAT#HNA' 8!NAM#$" # is of o(a(io* is i* (he pla*e of pape.

a c d

e f f

i I F

F m *



39/51

o

19. 8e(emi*e (he ma*i()de of *e( (o)e ac(i* o* (he od+ sho* i* each case ao)( (he i/e*

a>is of o(a(io*.

a c

d e f

h i

190. 8e(emi*e (he mome*( of folloi* foces ao)( (he specified poi*(s. %>pess +o) a*se i*

)*i( /ec(os^

i,^

j ,^

k. Also specif+ (he a>is of o(a(io* i* each case.

a

^^

2jiF +

ac(i* a(


40/51

191. $o*side a foce

+

^^

64 ji ac(i* o* a lae sphee ce*(ed a( oii*. -oce is ac(i* a( (he poi*(

is of o(a(io*.

RHTAT#HNA' 8!NAM#$" #


41/51

199. A (hi* ie is e*( (o fom a cic)la i* of adi)s R. The li*ea de*si(+ of (he ie /aies as k0= , 20 is passi* (ho)h is ce*(e a*d pepe*dic)la (o

is pla*e.

200. A (hi* )*ifom ie is e*( (o fom a spial hose e)a(io* is i/e* +:

20,0 is is + as sho* i* (he fi)e. Mass of (he

od is m a*d le*(h is l.

202. A (hi* s(eel ie is e*( i*(o (he shape sho*. 8e*o(i* (he mass pe )*i( le*(h of (he ie +

m, de(emi*e + diec( i*(ea(io* (he mome*( of i*e(ia of (he ie i(h espec( (o each of (he

coodi*a(e a>es. , +.

203. A fla( ec(a*)la pla(e has /aiale s)peficial de*si(+ i/e* + x0= , hee 0 is aco*s(a*( a*d > is (he dis(a*ce meas)ed alo* >a>is. is is



42/51

204. 8e(emi*e (he mome*( of i*e(ia of a* ellipse of semi a>es a a*d , ao)( is, a*dis. Ose (he pepe*dic)la a>is (heoem (o de(emi*e (he mome*( of i*e(ia of

(he ellipse ao)( a* a>is pepe*dic)la (o (he pla*e of (he ellipse (ho)h (he ce*(e.

205. 8e(emi*e (he mome*( of i*e(ia of a lami*a cic)la sec(o of adi)s R a*d mass M, maFi*

a* a*le of 600a( (he ce*(e, ao)( a* a>is passi* (ho)h (he ce*(e of (he o)(emos( im >

a*d pepe*dic)la (o (he pla*e of (he sec(o.

206. The mass of cic)la disc i* m. A cic)la hole is *o c)( i*(o i( as sho* i* (he fi)e. -i*d (he

mome*( of i*e(ia of (he emai*i* pa( ao)( a* a>is passi* (ho)h poi*( A pepe*dic)la

(o (he discs pla*e.

207. The s)face de*si(+ is. -i*d (he mome*( of i*e(ia of (he pla(e

ao)(:

i > a>is ii +a>is iii ;a>is

209. A fla( cic)la disc of adi)s R has /aiale de*si(+ i/e* + 2

0si= hee 0 is a

co*s(a*( a*d is (he a*le made i(h >a>is. -i*d (he mome*( of i*e(ia of (he disc ao)( a*

a>is passi* (ho)h i(s ce*(e, pepe*dic)la (o i(s pla*e.



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217. A ladde is es(i* o/e (he o)h all a*d o)h s)face. -i*d o)( (he a*le fo

e)ilii)m.

21. -i*d o)( mi*. fic(io* coefficie*( (o (opple (his he>ao* o* o)h s)face

219. -i*d o)( foce - e)ied (o mai*(ai* (he pla*F o/e (o olles.

220. -i*d o)( (he ma>. a*le fo e)ilii)m of hemisphee es(i* a( (he co*e of a oom, (aFe

fic(io* coefficie*( fo each s)face.

221. A disc of mass M a*d adi)s R is i* p)e olli* + (he applica(io* of foce - a( heih( h. 8ecide

ho (he fic(io* foce cha*es i(s diec(io* ..(. heih( of foce applica(io*.

222. 8isc)ss (he mi*im)m fic(io* coefficie*( fo oIec(s


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223. -i*d o)( (he mi*im)m fic(io* coefficie*( (o pe/e*( slippi*

224. -i*d o)( (he ma>im)m /al)e of T fo p)e olli* of spool. "pool ma+ e co*sideed as disc of

adi)s R a*d mass M.

225. -i*d o)( (he accelea(io* of pla*F a*d c+li*de a*d (hei fic(io* foces fo p)e olli*

226. A solid sphee a*d a (hi* spheical hoop of e)al mass m a*d adi)s R ae ha*essed (oe(he

+ ii* a*d fee (o oll i(ho)( slippi* do* (he i*cli*ed pla*e as sho*. Nelec(i* (he

mass of ii*, de(emi*e (he foce i* ii*. Ass)me fic(io*less eai*.

227. A ope is apped o/e (he o)h p)lle+ ad (ies (o o(a(e p)lle+. -ic(io* coefficie*( e(ee*

(hem is a*d (he a*le made + ope a( ce*(e is . -i*d o)( ho T1is ela(ed (o T2.

22. $o*side a solid sphee a*d c)e ae es(i* o* s)fficie*( o)h i*cli*ed s)face. 8isc)ss (he

*omal co*(ac( foce e(ee* (hem



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CH 'e/el is pepe*dic)la (o i(s pla*e a*d passi*(ho)h i(s ce*(e is placed o/e a*o(he disc of mome*( of i*e(ia #1o(a(i* i(h a* a*)la

/eloci(+ ao)( (he same a>is. The fi*al a*)la /eloci(+ of (he comi*a(io* of discs id

a( )

1

21

!

!! +

21

1

!!

!

+

c d21

1

!!

!

+

230. A solid sphee, a hollo sphee a*d a i* ae eleased fom (op of a* i*cli*ed pla*e

im)m accelea(io* do* (he pla*e is

fo


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236. H*e )a(e sec(o is c)( fom a )*ifom cic)la disc of adi)s R. This sec(o has mass M. #( is

made (o o(a(e ao)( a li*e pepe*dic)la (o i(s pla*e a*d passi* (ho)h i(s ce*(e of (he

oii*al disc. #(s mome*( of i*e(ia ao)( (he a>is of o(a(io* is

a2

2

1MR

2

4

1MR c

2

8

1MR d 22MR

237. A disc of mass M a*d adi)s R is olli* i(h a*)la speed o* a hoi;o*(al pla*e as sho*.The ma*i()de of a*)la mome*()m of disc ao)( (he oii* H is

a 2

2

1MR 2MR c

2

2

3MR d 22MR

23. A c)ical locF of side a is mo/i* i(h /eloci(+ vo* (he hoi;o*(al smoo(h pla*e as sho* i*

fi. #( hi(s a ide a( poi*( H. The a*)la speed of (he locF af(e i( hi(s H is

a

a

v

4

3

a

v

2

3c

a

v

2

3d eo

239. A pa(icle of mass m is eleased fom es( a( poi*( A falli* paallel (o /e(ical +a>is. #(s

a*)la mome*()m af(e falli* (ho)h dis(a*ce h ao)( H is

a g"ma 2 g"

a

m2 c

g"

mad

ag

m"

240. A c+li*de of adi)s R is spi**ed a*d (he* placed o* a* i*cli*ed ha/i* fic(io* coefficie*( ta= . The c+li*de co*(i*)es (o spi* i(ho)( falli* fo (ime

a

si3

0

g

R

si2

0

g

Rc

si

0

g

Rd

si

20

g

R



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241. A poi*( is mo/i* i* a cicle. The a(io of i(s a*)la /eloci(+ ao)( a poi*( o* (hecic)mfee*ce

of (he cicle a*d ao)( (he ce*(e of cicle is

a# 1 $ 2 %# 2 $ 1 c# 1$ d $1

242. A c+li*dical d)m is p)shed alo* + a oad of le*(h l. The d)m olls foad o* (he

o)*d a dis(a*ce of l=2. Thee is *o slippi* a( a*+ i*s(a*(. 8)i* (he pocess of p)shi* (he

oad, (he dis(a*ce mo/ed + (he ma* o* (he o)*d is

a l=2 3l=2 c l d No*e of (hese

243. A s(i* is apped ao)*d a c+li*de of mass M a*d adi)s R. The s(i* is p)lled /e(icall+

)pad (o pe/e*( (he ce*(e of mass fom falli* as (he c+li*de )*i*ds (he s(i*. -i*d (he

le*(h of (he s(i* )*o)*d he* (he c+li*de has eached a speed .

a# g

R 22

g

R

2

22

c g

R

4

22

d g

R

8

22

244. A )*ifom all of adi)s olls i(ho)( slippi* do* fom (he (op of sphee of adi)s R. The

a*)la /eloci(+ of (he all a( (he mome*( i( eaFs off (he sphee ill e is accodi* (o (he la 326 tt= . Lha( is (he mea*/al)e of a*)la /eloci(+ o/e (he (ime i*(e/al e(ee* ( 0 a*d (he (ime he* (he od+ comes

(o es(K

a 2 ad=s 7 ad=s c 3 ad=s d 4 ad=s

247. A solid sphee of adi)s R is p)lled + a foce - ac(i* a( (he (op of (he sphee as sho* i* (he

fi. Thee is *o slippi* a*+hee. LoF do*e + foce -, he* (he ce*(e of mass mo/es a

dis(a*ce sis



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a -s 2 -s c eo d2

3-s

24. The pla*F i* (he fi)e mo/es a dis(a*ce 100mm (o (he ih( hile (he ce*(e of mass of (he

sphee of adi)s 150mm mo/es dis(a*ce 75mm (o (he lef(. The a*)la displaceme*( of (he

sphee


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260. Poe s)pplied (o a pa(icle of mass 2F /aies i(h (ime as2

32

tP= a((, hee ( is i* sec. #f

/eloci(+ of pa(icle a( ( 0 is / 0. The /eloci(+ of pa(icle a( (ime ( 2sec ill e

a 1 m=s 4 m=s c 2 m=s d 22 m=s

261. To illiad alls of (he same si;e a*d mass ae i* co*(ac( o* a illiad (ale. A (hid all of (he

same si;e a*d mass s(iFes (hem s+mme(icall+ a*d emai*s a( es( af(e (he impac(. Thecoefficie*( of es(i()(io* e(ee* (he alls is

a 1=2 3=2 c 2=3 d 3=4

262. A co*s(a*( poe is s)pplied (o a o(a(i* disc. A*)la /eloci(+

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