To determine the Modulus of Rigidity of the material of a wire. IDENTIFY

1) A long iron WIRE suspended from a point at the center of a rod. 2) A cylindrical pendulum attached at the end of the wire. 3) An ADJUSTABLE SCREW at the point of suspension. This screw is turned to

adjust the length of the wire. The screw is opened and the wire is PULLED UP to DECREASE the length and PUSHED DOWN to INCREASE the length.

4) The STOP WATCH (learn the operation of the stop watch). DIAGRAM

THEORY Time period of torsional oscillation, T, of a body of moment of inertia I about the axis of suspension is given by

)1(2C

IT π=

Where, C is the moment of torsional couple per unit angle which again in terms of the rigidity modulus, η, is

)2(2

4

L

rC

ηπ=

Where, r is the radius and L is the length of the wire. For a cylindrical bob the moment of inertia is given by

)3(2

1 2MRI =

Where, M and R are the mass and the radius of the bob. From (1), (2) and (3), the working formula for the rigidity modulus is

= 242 2

18MR

rT

Lπη

PROCEDURE

1) The diameter of the wire is measured using a screw gauge. Take three readings. 2) The diameter of the cylinder is measured using slide calipers. Take three readings. 3) Measure the length of 40 cms using a METRE scale. Mark the length with a

chalk. Now adjust the length to 40cms by using the screw. FIX the screw TIGHTLY.

4) Give a twist of 300 to the cylindrical pendulum (DO NOT OSCILLATE LIKE SIMPLE PENDULUM). The pendulum undergoes torsional oscillation about its axis.

5) Measure the total time for FIFTY oscillations by using a stop watch. 6) TABULATE this time for lengths 40cms, 50cms, 60cms, 70 cms, and 80 cms. 7) Calculate the TIME PERIOD = Total Time/50. 8) Draw a graph of time period length (L – along x-axis) versus (T2 – along y-

axis) s. using the slope of the graph calculate the rigidity modulus from the given formula.

SUPPLIED DATA Weight of the cylinder =2.0 Kg. EXPERIMENTAL RESULTS

Table 1. Diameter of the suspension wire Least count of the screw gauge = ……… m.m No. of Obs. Diameter (2r) Mean Radius r

(m) Linear scale Circular scale Total (mm)

Table 2.Diameter of the cylinder: Vernier constant of slide calipers = ……….. c.m

No. of Obs. Diameter Mean Radius R (m) Linear scale Vernier scale Total (cm)

Table 3. Time period of oscillations: No. of Obs.

Length of the wire L

Time taken for 50 complete oscillations in sec

Mean time for 50 oscillations (t) in sec

Time period T=t/50

(sec)

T2

in sec2

i) ii)

CALCULATIONS- Obtain the value of L/T2 from the slope of the graph of time period length (L) versus (T2).

4

8

r

π(m-4)

2

2

1MR

(Kg.m2)

L/T2

(m.s-2) η (N/m2)

MAXIMUM PROPORTIONAL ERROR CALCULATIONS:

%100422%100 ×

+++=×r

r

T

T

R

R

L

L δδδδηδη

δr = least count of the screw gauge δR = Vernier constant of the slide calipers δT = 1 sec, δL = 0.1 c.m For maximum error use the least values