## APPARATUS REQUIRED

i) Maxwell’s needle.

ii) Screw gauge

iii) Meter scale

iv) Stopwatch

v) Given wire

vi) Physical balance and weight box.

## THEORY:

The modulus of Rigidity of the given wire is calculated by the following relation.

η = 2πl(m_{2}-m_{1}) l^{3} / r^{4}(T^{2}_{1}-T^{2}_{2})

Where, η = modulus of rigidity.

l= length of wire

M_{1} = Mass of hollow cylinder

M_{2} = mass of solid cylinder

T_{1} = Time period of solid cylinders on the innerside

T_{2} = Time period of solid cylinder on the outside

r= radius of wire

## OBSERVATION:

Table for determination of T_{1} and T_{2}

length of wire (l) =79cm =0.79m

length of maxwell’s needle (l) = (0.41) m

Mass of hollow cylinder (M_{1}) = 50 gm = 0.05kg

Mass of solid cylinder (M_{2}) = 250gm = 0.25kg

Radius of wire (r) = 45×10^{-5}/2 m

## CALCULATION

Modulus of rigidity (η) : 2π(m_{2}-m_{1})l^{2} / r^{4}(T^{2}_{1}-T^{2}_{2})

= 2π(0.25 -0.05) (0.41)^{2} / (45X10^{-5}/2)^{4} [(110.6)^{2}-(73.633)^{2}]

= 9.40×10^{9} N/m²

## PERCENTAGE ERROR

Standard value 7η = 1.7 × 10^{11} N/m^{2}

observative value (η) = 9.4×10^{9} N/m²

Here error = Standard value-observative value / Standard value X100%

= 94.5%

## RESULT:

Thus the modulus of rigidity of the given wire was found to be 1.40X 10^{9} N/m^{2}

## CONCLUSION

Thus the modulus of rigidity of the given wire can be determined by using Maxwell’s needle.