Question

A solid sphere of radius R and mass M is pulled by a force F acting at the top of the sphere as shown in figure. Friction coefficient is sufficient enough to provide rolling without slipping. (Given that ‘S’ being the displacement of centre of mass)

• A. Work done by force is FS.
• B. Work done by force is 2FS.
• C. Velocity of top point is equal to velocity of point of contact.
• D. Velocity of top point is two times velocity of centre of mass.

Answer 1

Answer: (C), (D)

Velocity of the top point is two times the velocity of the center of mass.

B Work done by the force is 2FS.

Given,

Force acting on the top point = F

Since the motion is pure rolling so the velocity of the lowest point will be zero

We can write,

$V_{lowestpoint}=V_{CM}-rw$

$Or,0=V_{CM}-rw$

$Or,V_{CM}=rw$

Now velocity of the topmost point is given as

$V_{topmost}=V_{CM}+rw$

$Or,V_{topmost}=rw+rw=2rw$

Now we can say that the velocity of the top point is 2 times the velocity of the center of mass.

Now,

If the CM will cover distance S then the top point will cover distance 2S.

So,

Work done by the top point is

$W=Force\times Displacement=2F\times S$

Hence the work done is 2FS