Determine Modulus of Rigidity Using Maxwell’s Needle | PDF

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(m₂-m₁) l³ / r⁴(T²₁-T²₂)

Where, η = modulus of rigidity.

 l= length of wire

M₁ = Mass of hollow cylinder

M₂ = mass of solid cylinder

T₁ = Time period of solid cylinders on the innerside

T₂ = Time period of solid cylinder on the outside

r= radius of wire

OBSERVATION: 

Table for determination of T₁ and T₂

length of wire (l) =79cm     =0.79m

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

Mass of hollow cylinder (M₁) = 50 gm  = 0.05kg

Mass of solid cylinder (M₂) = 250gm     = 0.25kg

Radius of wire (r) = 45×10^-5/2 m

CALCULATION

Modulus of rigidity (η) : 2π(m₂-m₁)l² / r⁴(T²₁-T²₂)

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

= 9.40×10⁹ N/m²

PERCENTAGE ERROR

Standard value 7η = 1.7 × 10¹¹ N/m²

observative value (η) = 9.4×10⁹ 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 10⁹ N/m²

CONCLUSION

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