Way to Success Model Question Paper · wtsteam [email protected] - 4 - A source emits a sound of frequency of 400 Hz. But the listener hears it to be 390 Hz. Then (a) The listener is

11th Physics Way to Success

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Way to Success Model Question Paper (Based on new Question pattern 2019)

,aw;gpay; / PHYSICS

Neuk;: 2.30 kzp ] [ nkhj;j kjpg;ngz;fs;: 70 Time Allowed: 2.30 Hours] [Maximum Marks: 70

gFjp – I / Part – I 15 x 1 = 15

(i) midj;J tpdhf;fSf;Fk; tpilaspf;fTk; (i) All questions are compulsory

tpdh vz; 1 Kjy; 4 tiu cs;stw;wpw;F kpfTk; Vw;Gila tpilapid vOjTk; /

Choose the most suitable answer from the questions 1 to 4

𝟏. (𝜇0𝜀0)−1

2 d; gupkhzj;ijf; fPo;f;fz;ltw;Ws; vJ ngw;wpUf;Fk;?

(a) ePsk; (b) fhyk; (c) jpirNtfk; (d) tpir

The dimension of (𝜇0𝜀0)−1

2 is

(a) Length (b) time (c) velocity (d) force

2. நேர்க்ந ோட்டு உந்தம் = நிறை × ______________

Linear Momentum = Mass × ____________

3. ];NfyhH ngUf;fy;𝐴 . �⃗⃗� = ____________________

Scalar Quantity. 𝐴.⃗⃗⃗⃗ 𝐵 ⃗⃗⃗⃗ = ____________________

4. அலைகளின் வேகமானது (v) = _______________ Velocity of the wave is (v) = ________________

tpdh vz; 5 Kjy; 6 tiu cs;stw;iw nghUj;jTk;

5. gj;jp I gj;jp II

(A) அதி பட்ச நேறை (p) நசமிப்பு நிறைஆற்ைல்

(B) பபோருளின் திறசநே ம் இரட்டிப்போகும் (q) சுருளின் மோறிலி இருமடங்கு

(C) சுருளின் நீளம் போதியளவு (r) இயக் ஆற்ைல் ேோன்கு மடங ோகும்

(D) சுருளின் இழுத்தல் அல்ைது நீட்டித்தல் (s) விறச மற்றும் இடப்பபயர்ச்சிக் ோன ந ோணம்

(a) A-s, B-r, C-q , D -p (b) A-p, B-q, C-r , D -s

(c) ) A-s, B-r, C- p, D -q (d) A-p, B-r, C-s , D - q

A

Namma Kalvi

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Column I Column II

(A) Work done is maximum (p) Potential energy is stored

(B) Velocity of the body is doubled (q) spring constant becomes twice

(C) Length of the spring is halved (r) K. E. becomes four times

(D) On compressing or stretching a spring (s) Angle between force and displacement


(c) ) A-s, B-r, C- p, D -q (d) A-p, B-r, C-s , D - q

6. gj;jp I gj;jp II

(A) ஒரு பபோருளின் இயக் ஆற்ைல் எதிர்மறை இல்றை (p) இயக் ஆற்ைல் 300% அதி ரிப்பு

(B) சீரோன ேட்ட இயக் ம் (q) இயக் ஆற்ைல் அதி ரித்தல்

(C) ோற்றில் பைந்து ேரும் துப்போக்கி குண்டு (r) இயக் ஆற்ைல் ஒரு மோறிலி

(D) பபோருளின் உந்தம் 100% அதி ரித்தல் (s) சரி


(c) ) A-p, B-r, C- q, D -s (d) A-s, B-r, C-q , D - p

Column I Column II

(A) K.E. of a body cannot be negative (p) K.E. increases by 300%

(B) In a uniform circular motion (q) K.E. increases

(C) A shot fired from a gun explodes in air (r) K.E. remains constant

(D) Momentum of a body is increased by 100% (s) True


(c) ) A-p, B-r, C- q, D -s (d) A-s, B-r, C-q , D - p

tpdh vz; 7 - y; cs;stw;iw rhpah> jtwh vdf;$wTk; /

Say TRUE or FALSE from the question number 7

7. nrq;Fj;J mr;R Njw;wk; Iz = Ix + Iy

Perpendicular axis theorem Iz = Ix + Iy

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tpdh vz; 8 Kjy; 12 tiu cs;stw;wpw;F kpfTk; Vw;Gila tpilapid vOjTk; / Choose the most suitable answer from the questions 8 to 12

8. திண்பபோருள் ஒன்று ந ோண உந்தம் L உடன் சுழல்கிைது. இதன் இயக் ஆற்ைல்

போதியோனோல் ந ோண உந்தமோனது

(a) L (b) 𝐿

2 (c) 2L (d)

𝐿

√2

A rigid body rotates with an angular momentum L. If its kinetic energy is halved, the angular momentum becomes,

(a) L (b) 𝐿

2 (c) 2L (d)

𝐿

√2

9 . eல்லியல்பு ேோயு ஒன்று சமனிறையில் உள்ள நபோது பின்ேரும் அளவு ளில் எதன்

மதிப்பு சுழியோகும்?

(a) rms நே ம் (b) சோரசரி நே ம்

(c) சரோசரி திறசநே ம் (d) மி வும் சோத்தியமோன நே ம்

A sample of ideal gas is at equilibrium which of the following quantity is zero?

(a) rms speed (b) average speed (c) average velocity (d) most probable speed

10. jdp rPupir ,af;fj;jpy; xU KO miytpw;fhd ,lg;ngaHr;rpf;F vjpuhd KLf;fkhdJ Vw;gLj;JfpwJ.

(a) ePs;tl;lk; (b) tl;lk; (c) gutisak; (d) NeHf;NfhL

In a simple harmonic oscillation, the acceleration against displacement for one complete oscillation will be

(a) an ellipse (b) a circle (c) a parabola (d) a straight line.

11. xyp %yk; xd;W 400 Hz mjpHntz;zpy; xypia ckpo;fpwJ. Mdhy; mij Nfl;gtH 340 Hz mjpHntz;zpy; Nfl;fpwhH vd;why;

(a) Nfl;gtH xyp %yj;ij Nehf;fp efHfpd;whH

(b) xyp %yk; Nfl;gtiu Nehf;fp efHfpwJ

(c) Nfl;gtH xyp %yj;ij tpl;L tpyfp nry;fpwhH

(d) Nfl;gtUf;F fhJ FiwghL



A source emits a sound of frequency of 400 Hz. But the listener hears it to be 390 Hz. Then

(a) The listener is moving towards the source

(b) The source is moving towards the listener

(c) The listener is moving away from the source

(d) The listener has a defective ear.

12. ghapy; tpjp nray;gLtJ

(a) gUkd; khwh epfo;T (b) ntg;gepiy khwh epfo;T

(c) mOj;jk; khwh epfo;T (d) ntg;g gupkhw;wkpy;yh epfo;T

Boyle's Law is applicable in

(a) Isochoric process (b) Isothermal process

(c) Isobaric Process (d) Adiabatic process

tpdh vz; 13 Kjy; 15 tiu $w;W (A) kw;Wk; fhuzk; (R) - f;fhd tpilapid vOjTk; /

Choose the Assertion and Reason type questions from question number 13 to 15

(a) (A) kw;Wk; (R) ,uz;Lk; cz;ikahFk;. (R) vd;gJ (A) vd;gjd; rhpahd tpsf;fkhFk;

(b) (A) kw;Wk; (R) ,uz;Lk; cz;ikahFk;. (R) vd;gJ (A) vd;gjd; rhpahd tpsf;fk; my;y

(c) (A) cz;ikahFk; (R) vd;gJ jtW MFk;.

(d) (A) vd;gJ jtwhFk;. (R) vd;gJ cz;ikahFk;

(A) Both Assertion and Reason are true and the Reason is correct explanation of the Assertion

(B) Both Assertion and Reason are true but the Reason is not a correct explanation of the Assertion

(C) Assertion is true but the Reason is false.

(D) Both Assertion and Reason are false.

13. $w;W (A): ஒரு குறிப்பிட்ட வேரத்தின் வேகத்தில் அதன் வேகம் பூஜ்ஜியமாக இருந்தாலும் ஒரு பபோருளில் முடுக்கம் ஏற்படைாம்.

fhuzk; (R): இயக்கம் அதன் திலை இயக்கத்லத மாற்றியலமக்கும் வபாது பபோருளின் மீதும் இருக்கும்.

. (a) A (b) B (c) C (d) D

Assertion: A body can have acceleration even if its velocity is zero at a given instant of time.

Reason: A body is momentarily at rest when it reverses its direction of motion.

(a) A (b) B (c) C (d) D

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14. $w;W (A): xU nghUs; epiyahd Ntfj;ij ngw khWglf;$ba jpirNtfk; Ntz;Lk;. fhuzk@ (R): Ntfk; vd;gJ ];NfyhH msT. Mdhy; jpirNtfk; ntf;lhH msT. (a) A (b) B (c) C (d) D

Assertion: An object can have constant speed but variable velocity.

Reason: Speed is a scalar but velocity is a vector quantity.

(a) A (b) B (c) C (d) D

15. $w;W (A): பபோருளின் எதிர்மலற முடுக்கம் பபோருளின் "வேகப்படுத்துதல்" உடன் ததாடர்புலடயதாக இருக்கைாம்

fhuzk; (R): xU efUk; nghUspd; Ntfk; mjpfkhf ,Ug;gpd; mjd; jpirapypUe;J khWgl;L ,Uf;Fk;.

(a) A (b) B (c) C (d) D

Assertion: A negative acceleration of a body can be associated with a "speeding up" of the body.

Reason: Increase in speed of a moving body is independent of its direction of motion.

(a) A (b) B (c) C (d) D

gFjp – II / Part – II 6 x 2 = 12 vitNaDk; 6 tpdhtpw;F tpilaspf;fTk;. Answer any six questions. 16. gupkhz gFg;gha;tpd; tuk;Gfs; ahit?

What are the limitations of dimensional analysis?

17. திறசநே ம் மற்றும் சரோசரி திறசநே ம் இேற்றிற்கிறடநயயோன நேறுபோடு ள் யோறே?

What is the difference between velocity and average velocity?

18. epa+l;ldpd; ,uz;lhtJ tpjpiaf; $Wf.

State Newton's second Law.

19. kPl;rp kw;Wk; kPl;rpaw;w Nkhjypd; rpwg;gpay;Gfis tpsf;Ff.

Explain the characteristics of elastic and inelastic collision.

20. jpUg;Gj;jpwdpd; jj;Jtj;ijf; $Wf.

State principle of moments.

21. epa+l;ldpd; <Hg;gpay; nghJ tpjpia jUf.

State Newton's Universal law of gravitation.



22. gha;rhd; tpfpjj;ij $Wf.

Define Poisson's ratio

23. jd; ntg;g Vw;Gj; jpwd; vd;why; vd;d? mjd; myif vOJf.

Define specific heat capacity and give its unit.

24. FWf;fiy vd;why; vd;d? XH vLj;Jf;fhl;L jUf.

What are transverse waves? Give one example.

gFjp – III / Part – III 6 x 3 = 18 vitNaDk; 6 tpdhtpw;F tpilaspf;fTk;. tpdh vz; 33f;F fz;bg;ghf tpilaspf;fTk;. Answer any six questions. Question No.33 is compulsory

25. Kf;fpa vz;ZWf;fis fzf;fpLtjpd; tpjpfisj; jUf.

Write the rules for determining significant figures.

26. ,uz;L ntf;lhHfspd; ];NfyhH ngUf;fy; gw;wp rpWFwpg;G tiuf.

Write a short note on the scalar product between two vectors.

27. 20 Kg epiwAs;s nghUs; kPJ 50 N tpir glj;jpy; fhl;bathW nray;gLfpwJ. x > y jpirfspy; nghUspd; KLf;fq;fisf; fhz;f.

A force of 50 N act on the object of mass 20 Kg. shown in the figure. Calculate the acceleration of the object in x and y directions.

28. எறட - tiuaW.

Define weight.

29. kpjj;jy; tpjpiaf; $Wf.

State the law of floatation.

30. ruhrup Nkhjypilj; J}uj;ij ghjpf;Fk; fhuzpfs; ahit?

List the factors affecting the mean free path.

31. gpnusdpad; ,af;fj;jpid tpsf;Ff.

Describe the Brownian motion

32. jdp Crypd; tpjpfisj; jUf.

State the laws of simple pendulum?

33. lhg;sH tpisit tpsf;Ff.

Explain Doppler effect.

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gFjp – IV / Part – IV 5 x 5 = 25

(i) midj;J tpdhf;fSf;Fk; tpilaspf;fTk; (i) All questions are compulsory

34. gupkhzj;jpd; xUgbj;jhd newpKiw vd;why; vd;d? mjd; gad;fs; ahit? vLj;Jf;fhl;L jUf. (my;yJ)

Jfnshd;wpd; epiy ntf;lupd; ePsk; 1 m . mJ X mr;Rld; 300 Nfhzj;jpy; cs;sJ vdpy;> epiyntf;lupd; x kw;Wk; y $Wfspd; ePs;q;fisf; fhz;f.

Explain the Principle of homogeneity of dimensions. What are its uses? Give example. . (Or)

The position vectors particle has length 1m and makes 300 with the x - axis. What are the lengths of the x and y components of the position vector?

35. xU ikatpirfs; vd;why; vd;d? yhkpapd; Njw;wj;ijf; $W. (my;yJ)

2Kg gSit 10 m cauj;jpw;F J}f;Fk; 30 N tpirapdhy; nra;ag;gl;l Ntiyiaf; fzf;fpLf

What are concurrent forces? State Lami's theorem. (Or)

Calculate the work done by a force of 30 N in lifting a load of 2Kg to a height of 10 m (g = 10 ms-2

36. irf;fps; xl;LgtH tisTg;ghijia flf;f KaYk; NghJ rha;tjw;fhd; fhuzk; vd;d? nfhLf;fg;gl;l jpirNtfj;jpw;F irf;fps; xl;LgtH rhAk; Nfhzj;jpw;fhd; rkd;ghl;il ngWf.

(my;yJ)

<Hg;G epiy Mw;wYf;fhd Nfhitiaj; jUtp.

Explain why a cyclist bends while negotiating a curve road? Arrive at the expression for angle of bending for a given velocity. (Or)

Derive the expression for gravitational potential energy.

37. kPl;rp Fzfj;jpd; tiffis tpsf;Ff. (my;yJ)

fhHNdh ntg;g ,ae;jpuj;ijg; gw;wp tpupthf tpsf;Ff.

Explain the different types of modulus of elasticity. . (Or)

Explain in detail Carnot heat engine.

38. thAf;fspd; ,af;ftpaw; nfhs;iff;fhd vLNfhs;fs; ahit? (my;yJ)

Rukhdp vd;why; vd;d? mjd; mikg;G kw;Wk; Ntiy nra;Ak; tpjj;ij tptup. Rukhdpiag; gad;gLj;jp ,irf;fitapd; mjpHntz;iz vt;thW msg;gha;?

Write down the postulates of kinetic theory of gases. . (Or)

What is a sonometer? Give its construction and working. Explain how to determine the frequency of turning fork using sonometer.

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Way to Success Model Question Paper ,aw;gpay; / PHYSICS

Answer Key (Based on new Question pattern 2019)

gphpT – I / SECTION – I

1 (c) 9 (b)

2 jpirNtfk; velocity

10 (d)

3 𝑨𝑩 𝒄𝒐𝒔𝜽; 11 (c)

4 v = f λ 12 (b)

5 (𝒂) 13 (a)

6 (𝒅) 14 (b)

7 (d) 15 (c)

8 (d)

gFjp – II / Part – II 16)

1. This method gives no information about the

dimensionless constants in the formula like 1, 2,…….𝝅, e, etc.

2. This method cannot decide whether the given quantity is a vector or a scalar.

17)

Average velocity = 𝑫𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕

𝑻𝒊𝒎𝒆 𝒊𝒏𝒕𝒆𝒓𝒗𝒂𝒍 = 𝒗𝒂𝒗𝒈 ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ =

∆𝒓⃗⃗ ⃗⃗

∆𝒕

Velocity �⃗⃗� = 𝐥𝐢𝐦∆𝒕 →𝟎

∆𝒓⃗⃗ ⃗⃗

∆𝒕 =

𝒅𝒓⃗⃗⃗⃗ ⃗

𝒅𝒕

A

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18)

The force acting on an object is equal to the rate of change of its momentum.

19)

Elastic:- i) Total momentum is conserved ii) Total kinetic energy is conserved iii) Force involved are conservative forces iv) Mechanical energy is not dissipated

In Elastic Collision:- i) Total momentum is conserved ii) Total kinetic energy is not conserved iii) Forces involved are non - conservative forces iv) Mechanical energy is dissipated in the heat, sound etc.

20)

According to the principle of moments, a body will be in rotational equilibrium if algebraic sum of the moments of all forces acting on the body, about a fixed point is zero.

It means for rotational equilibrium of a body sum of anticlockwise moments about a fixed point is equal to the sum of clockwise moments about the same point.

21)

Newton's law of gravitation state that, a particle of mass M1 attracts any other particle of mass M2 in the universe with an attractive force. The strength of this force of attraction was found to be directly proportional to the product of their masses and is inversely proportional to the square of the distance between them.



22)

The ratio of lateral strain to longitudinal strain is called Poisson's ratio.

𝝁 = 𝐥𝐚𝐭𝐞𝐫𝐚𝐥 𝐬𝐭𝐫𝐚𝐢𝐧

𝐥𝐨𝐧𝐠𝐢𝐭𝐮𝐝𝐢𝐧𝐚𝐥 𝐬𝐭𝐫𝐚𝐢𝐧 . No

unit. No dimensions.

23)

Specific heat capacity of a substance is defined as the

amount of heat energy required to raise the temperature of 1 kg of a substance by 1 kelvin or 10C. Its SI unit is J Kg-1 K-1.

24)

In transverse wave motion, the constituents of the medium oscillate or vibrate about their mean positions in a direction perpendicular to the direction of propagation of waves. Example: Light (Electromagnetic waves)

gFjp – III / Part – III 25)

Rule Example

1. All non - zero digits are significant

2. all zeros between two non-zero digits are significant

3. All zeros to the right of a non - zero digit but to the left of a decimal point are significant.

4. a) the number without a decimal point, the terminal or trailing zero(s) are not significant.

b) All zeros are significant if they come from a measurement.

1342 has four significant figures

2008 has four significant figures

30700. Has five significant figures

a) 30700 has three significant figures

b) 30700m has five significant figures

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26)

The scalar product or dot product of two vectors is defined as the product of the magnitudes of both the vectors and the cosine of the angle between them.

Thus if there are two vectors 𝐴 ⃗⃗ ⃗ 𝑎𝑛𝑑 �⃗� having an angle 𝜃 between them, then their scalar product is defined as

𝑨 ⃗⃗ ⃗ . �⃗⃗� = 𝑨𝑩 𝒄𝒐𝒔𝜽

Here, A and B are magnitudes of 𝐴 ⃗⃗ ⃗ 𝑎𝑛𝑑 �⃗�

27)

28)

Objects on Earth experience the gravitational

force of Earth. The gravitational force acting on an

object of mass m is mg. This force always acts

downwards towards the centre of the Earth.

When we stand on the floor, there are two forces,

acting downwards and the other is the normal

force exerted by the floor upwards on us to keep

us at rest. The weight of an object W is defined as

the downward force whose magnitude /w is equal

to that of upward force that must be applied to the

object to hold it at rest or at constant velocity

relative to the earth. The direction of weight is in

the direction of gravitational force. So the

magnitude of weight of an object is denoted as W

= N = mg. Note that even though magnitude of

weight is equal to mg, it is not same as

gravitational force acting on the object.



29)

The law of floatation states that a body will float in a liquid, if weight of the liquid displaced by the immersed part of the body is at least equal to or greater than the weight of the body.

Ex: The apparent weight of the floating block is equal to zero because the weight of the block acting vertically downwards is balanced by the buoyant force acting on the block upwards.

30)

𝝀

= 𝟏

√𝟐𝝅𝒅𝟐𝒏 (𝒐𝒓)

𝑲𝑻

√𝟐𝝅𝒅𝟐𝑷 (𝒐𝒓)

𝒎

√𝟐𝝅𝒅𝟐𝑷

The average distance travelled by the molecule between collisions is called mean free path (λ)

𝝀 = 𝟏

√𝟐𝝅𝒅𝟐𝒏 (𝒐𝒓)

𝑲𝑻

√𝟐𝝅𝒅𝟐𝑷 (𝒐𝒓)

𝒎

√𝟐𝝅𝒅𝟐𝑷

1. Mean free path increases with increasing temperature. As the temperature increases, the average speed of each molecule will increase. It is the reason why the smell of hot sizzling food reaches several meter away than smell of cold food. 2. Mean free path increases with decreasing pressure of the gas and diameter of the gas molecules.



31)

In 1827, Robert Brown, a botanist reported that grains of

pollen suspended in a liquid moves randomly from one

place to other. The random (Zig - Zag path) motion of

pollen suspended in a liquid is called Brownian motion. In

fact we can observe the dust particle in water moving in

random directions. This discovery puzzled scientists for

long time. There were a lot of explanations for pollen or

dust to move in random directions but none of these

explanations were found adequate.

After a systematic study, Wiener and Gouy proposed that

Brownian motion is due to the bombardment of suspended

particles by molecules of the surrounding fluid. But during 19th

century people did not accept that every matter is made up of

small atoms or molecules. In the year 1905, Einstein gave

systematic theory of Brownian motion based on kinetic theory

and he deduced the average size of molecules.

According to kinetic theory, any particle suspended in a liquid

or gas is continuously

bombarded from all the

directions so that the mean free

path is almost negligible. This

leads to the motion of the

particles in a random and zig–

zag manner as shown in Figure.

But when we put our hand in water it causes no random motion

because the mass of our hand is so large that the momentum

transferred by the molecular collision is not enough to move

our hand.

32)

Laws of simple pendulum

i) Law of length: For a given value of acceleration due to

gravity, the time period of a simple pendulum is

directly proportional to the square root of length of the

pendulum T 𝛼 √𝑙

ii) Law of acceleration: For a fixed length the time period

of a simple pendulum is inversely proportional to

square root of acceleration due to gravity T 𝛼 1

√𝑔

iii) The time period of oscillation is independent of mass of

the bob and amplitude of oscillation.

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33)

When the source and the observer are in relative motion with respect to each other and to the medium in which sound propagates, the frequency of sound wave observed is different from the frequency of the source. This phenomenon is called Doppler Effect.

The frequency perceived by the observer is known as apparent frequency. It may be less than or greater than the actual frequency emitted by the sound source. The difference depends on the relative motion between the source and observer.



gFjp – IV / Part – IV

34)

Principle of homogeneity of dimensions The principle of homogeneity of dimensions states that the dimensions of all the terms in a physical expression should be the same. For example, in the physical

expression v2 = u2 + 2as, the dimensions of v2, u2 and 2 as are the same and equal to [L2T-2]. This method is used to i) Convert a physical quantity from one system of units to another. ii) Check the dimensional correctness of a given physical equation. iii) Establish relations among various physical quantities. To convert a physical quantity from one system of units to another This is based on the fact that the product of the numerical values (n) and its corresponding unit (u) is a constant. i.e, n [u] = constant (or) n1[u1] =

n2[u2].

Consider a physical quantity which has dimension ‘a’ in mass, ‘b’ in length and ‘c’ in time. If the fundamental units in one system are M1, L1 and T1 and the other

system are M2, L2 and T2 respectively, then we can

write,𝒏𝟏[𝑴𝟏𝒂 𝑳𝟏

𝒃 𝑻𝟏𝒄] = 𝒏𝟐[𝑴𝟐

𝒂 𝑳𝟐𝒃 𝑻𝟐

𝒄]. We have thus converted the numerical value of physical quantity from one system of units into the other system.

Let OA is position vector of particle has length 1m and makes 30° with the x - axis. In attachment it is clearly shown in figure OB is the component of OA along x axis. and OD is the component of OA along y - axis. In ∆OAB , Apply , cos30° = OB/OA OB = OAcos30° = 1 × √3/2 = 1.732/2 = 0.866 m Similarly, sin30° = AB/OA ∵ AB = OD So, sin30° = OD/OA OD = OAsin30° = 1 × 1/2 = 0.5 m Hence, component of OA along x- axis = 0.866 m Component of OA along y-axis = 0.5 m

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35)

W = இடப்பெயர்ச்சி × விசை

வேசை = விசை = 30 N

இடப்பெயர்ச்சி = 10 m

W = 10 m × 30 N = 300J

we know that w = displacement × force

so, here work done = force = 30N

displacement = 10m

W = 10 m × 30 N = 300J



36)

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The gravitational force is a conservative force. Consider a mass

𝑚1 fixed in its psition the position vector of mass 𝑚2 is 𝑟 . Let

𝑚2 be moved through a small distance d𝑟 . Work done dW

= �⃗⃗� 𝒆𝒙𝒕. 𝒅𝒓⃗⃗⃗⃗ ⃗. The work is done against the gravitational force.

Hence |�⃗⃗� 𝒆𝒙𝒕. | = |𝑭𝑮⃗⃗ ⃗⃗ | =

𝑮𝒎𝟏𝒎𝟐

𝒓𝟐 , dW = 𝑮𝒎𝟏𝒎𝟐

𝒓𝟐 𝒓.̂ 𝒅𝒓⃗⃗⃗⃗ ⃗ = 𝑮𝒎𝟏𝒎𝟐

𝒓𝟐 𝒅𝒓⃗⃗⃗⃗ ⃗

The total work done for displacing 𝑚2 from �̀� 𝑡𝑜 𝑟 𝑖𝑠

W = ∫ 𝒅𝑾 = 𝒓

�̇́�∫


𝒓𝟐 𝒅𝒓⃗⃗⃗⃗ ⃗ = 𝒓

�̇́�− (


𝒓 )

�́�

𝒓

= - 𝑮𝒎𝟏𝒎𝟐

𝒓+


�́� =

U(r) - U(�́�)

Case 1: If r < �́�: The mass 𝑚2 is attracted by 𝑚1

and it can move from r to �́� without any external

work. Work is done by the system and it spends its

internal energy. Hence work done is said to be

negative.

Case 2: If r > �́�: work has to be done against gravity

to move 𝑚2 and 𝑚1 from r to �́�. Work is done on

the system by external force. Hence work done is

positive.

If 𝑟 = ∞, 𝑈 ( 𝑟) = 0,𝑊 = ́́ = - 𝐺𝑚1𝑚2

𝑟 . The

gravitational potential energy of a system of two

masses 𝑚1 and 𝑚2 separated by a distance r is

defined as the amount of work done to bring the

mass 𝑚2 from infinity to a distance r assuming 𝑚1

to be fixed in its position. U(r) = - 𝐺𝑚1𝑚2

𝑟. It is

always negative. it is a scalar quantity. Its unit is

joule. Its dimensions are M𝐿2𝑇−2.



37)

There are three types of elastic modulus

(a) Young's modulus (b) Bulk modulus

(c) Rigidity modulus

a) Young's modulus: when a wire is stretched or compressed, then the

ratio between tensile stress and tensile strain is defined as Young's

modulus.

Young's modulus = 𝑻𝒆𝒏𝒔𝒊𝒍𝒆 𝒔𝒕𝒓𝒆𝒔𝒔 (𝒐𝒓)𝒄𝒐𝒎𝒑𝒓𝒆𝒔𝒔𝒊𝒗𝒆 𝒔𝒕𝒓𝒆𝒔𝒔

𝑻𝒆𝒏𝒔𝒊𝒍𝒆 𝒔𝒕𝒓𝒂𝒊𝒏 (𝒐𝒓)𝒄𝒐𝒎𝒑𝒓𝒆𝒔𝒔𝒊𝒗𝒆 𝒔𝒕𝒓𝒂𝒊𝒏

Y = 𝝈𝒕

𝜺𝒕 (𝒐𝒓) 𝒀 =

𝝈𝒄

𝜺𝒄 . S.I. Unit of Young's modulus is N𝒎−𝟐 (or)

Pascal.

b) Bulk modulus: Bulk modulus is defined as the ratio of volume

stress to the volume strain.

Bulk modulus K = 𝑽𝒐𝒍𝒖𝒎𝒆 𝒔𝒕𝒓𝒆𝒔𝒔

𝑽𝒐𝒍𝒖𝒎𝒆 𝒔𝒕𝒓𝒂𝒊𝒏

Volume stress = 𝝈𝒏 = 𝑭𝒏

∆𝑨= ∆𝐏, Change in

pressure.

Volume strain = 𝜺𝒗 = ∆𝑽

𝑽

∴ Bulk modulus K = - 𝝈𝒏

𝜺𝒗= −

∆𝑷∆𝑽

𝑽

The negative sign means that when pressure is

applied on the body, its volume decreases. Its

unit is N𝒎−𝟐 (or) Pascal.

Gases have small value of bulk modulus than

solids.

Compressibility: the reciprocal of the bulk

modulus is called compressibility. It is

defined as the fractional change in

volume per unit increase in pressure.

Compressibility C = 𝟏

𝑲= −

𝜺𝒗

𝝈𝒏= −

∆𝑽

𝑽

∆𝑷

Since, gases have small value of bulk modulus

than solids, their values of compressibility is

very high.

C) Rigidity modulus: 𝜼𝑹 =

𝑺𝒉𝒆𝒂𝒓𝒊𝒏𝒈 𝒔𝒕𝒓𝒆𝒔𝒔

𝒂𝒏𝒈𝒍𝒆 𝒐𝒇 𝒔𝒉𝒆𝒂𝒓 (𝒐𝒓) 𝒔𝒉𝒆𝒂𝒓𝒊𝒏𝒈 𝒔𝒕𝒓𝒂𝒊𝒏

Shearing stress 𝝈𝑺 =

𝒕𝒂𝒏𝒈𝒆𝒏𝒕𝒊𝒂𝒍 𝒇𝒐𝒓𝒄𝒆

𝒂𝒓𝒆𝒂 𝒐𝒗𝒆𝒓 𝒘𝒉𝒊𝒄𝒉 𝒊𝒕 𝒊𝒔 𝒂𝒑𝒑𝒍𝒊𝒆𝒅 =

𝑭𝒕

∆𝑨

The angle of shear or shearing strain 𝜺𝒔 =

𝒙

𝒉= 𝜽

Rigidity modulus 𝜼𝑹 = 𝝈𝒔

𝜺𝒔 =

𝑭𝒕

∆𝑨𝒙

𝒉

= 𝑭𝒕

∆𝑨(𝜽)

S.I. unit of rigidity modulus is N𝒎−𝟐 (or)

Pascal.

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38)

1. All the molecules of a gas are identical, elastic

spheres.

2. The molecules of different gases are different.

3. The number of molecules in a gas is very large and

the average separation between them

is larger than size of the gas molecules.

4. The molecules of a gas are in a state of continuous

random motion.

5. The molecules collide with one another and also

with the walls of the container.

6. These collisions are perfectly elastic so that there is

no loss of kinetic energy during collisions.

7. Between two successive collisions, a molecule

moves with uniform velocity.

8. The molecules do not exert any force of attraction

or repulsion on each other except during collision. The

molecules do not possess any potential energy and the

energy is

wholly kinetic.

9. The collisions are instantaneous. The time spent by

a molecule in each collision is very small compared to

the time elapsed between two consecutive collisions.

10. These molecules obey Newton’s laws of motion

even though they move randomly.



Sono means sound related, and sonometer implied

sound related measurements. It is a device for

demonstrating the relationship between the

frequency of the sound produced in the transverse

standing wave in a string and the tension, length and

mass per unit length of the string. Therefore, using

this device, we can determine the following

quantities.

a) The frequency of the turning fork or frequency of

alternating current

b) The tension in the string.

c) The unknown hanging mass

Construction:

The sonometer is made up of a hollow box which is

one meter long with a uniform metallic thin string

attached to it. One end of the string is connected to a hook and the other end is connected to a weight hanger through a pulley as shown in figure. Since only one string is used, it is also known as monochord. The weights are added to the free end of the wire to increase the tension of the wire. Two adjustable wooden knives are put over the board and their positions adjusted to change the vibrating length of the stretched wire.

Working:

A transverse stationary or standing wave is produced and hence, at the knife edges P and q, nodes are formed. In between the knife edges, anti-nodes are formed

.

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Documents

Way to Success Model Question Paper · wtsteam [email protected] - 4 - A source emits a sound of frequency of 400 Hz. But the listener hears it to be 390 Hz. Then (a) The listener is