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A uniform thin cylindrical disc of mass ...

A uniform thin cylindrical disc 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 Fig. 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 unstretched length of each spring is `L`. The disc is initially at its equilibrium position with its centre of mass (`CM`) at a distance `L` from the wall. The disc rolls without slipping with velocity `V_(0)=V_(0)hati`. The coefficient of friction is `mu`.

The net external force acting on the disc when its centre of mass is at displacement `x` with respect to its equilibrium position is

A

`-kx`

B

`-2kx`

C

`-(2kx)/(3)`

D

`-(4kx)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
For linear motion of disc
`F_("net") = Ma = - 2kx + f`
where `f =` frictional force
For rolling motion
`fR = - ((MR^(2))/(2))(alpha) = -((Ma)/2)R`
`rArr f = -(Ma)/(2) = - (F_("ext"))/(2)`
Therefore `F_(ext) = - 2kx - (F_("ext"))/(2) = -(4kx)/(3)`
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