Question

A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in horizontal plane. The un-stretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity $\overrightarrow{V_0}=V_0\hat{i}$. The coefficient of friction is $\mu$.
The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is?

• A. $-kx$
• B. $-2kx$
• C. $-\frac{2kx}{3}$
• D. $-\frac{4kx}{3}$

Answer 1

The correct option is D $-\frac{4kx}{3}$

$2kx-f=ma$

$⟹f\cdot R=I\alpha$

$a=R\alpha$

$⟹ma=-4\frac{kx}{3}$