Question

Two metallic cylinder made of same material and radii r and 2r are joined.if top end is fixed and lower end of the cylinder b is twisted by an angle theta then angle of twist for cylinder a is

Answer 1

Given:

Two metallic cylinders,

Radius of cylinder 1 = r

Radius of cylinder 2 = 2r

To find:

The twist

Solution:

Clockwise torque produced by cylinder 2 =  Anticlockwise torque produced by cylinder 1

Torque = η π ( r )^4 θ2 / 2 l

Substituting and equating,

We get,

η π ( 2r )^4 θ2 / 2 l = η π ( r )^4 θ2 / 2 l

θ1 = 16 θ2  

Twisted angle = θ1 + θ2  

Substituting,

θ2 + 16 θ2 = θ

Hence, The angle of twist,

θ1 = 16 / 17 θ

θ2  = θ / 17

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