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Question

A uniform cylinder of mass M and radius R is released from rest on a rough inclined surface of inclination θ with the horizontal as shown in figure. As the cylinder rolls down the inclined surface, the maximum elongation in the spring of stiffness k is

Initially spring is in its natural length.
  1. 2Mgsinθk
  2. Mgsinθk 
  3. None of these
  4. 34Mgsinθk


Solution

The correct option is A 2Mgsinθk
In pure rolling,
Work done by static friction is zero.
Applying energy conservation principle at maximum elongation,
Work done by gravity =Change in potential energy of spring
12kx2=Mgxsinθ
x=2Mgsinθk

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