A solid sphere of mass `M` and radius `R` is initially at rest. Solid sphere is gradually lowered onto a truck moving with constant velocity `v_(0)`

What is the final speed of the sphere's centre of mass m ground frame when eventually pure rolling sets in

Options

A. `5/7v_(0)`
B. `2/7v_(0)`
C. `7/5v_(0)`
D. `7/2v_(0)`

Answer

B

Explanation

In reference frame of truck, the angular momentum is conserved about `P` i.e.
`MvR=Mv_(0)R=2/5MR^(2)omega`……….i

`v=Romega`…………ii
On solving eqn i and ii we get
`v=5/7v_(0)`
Note that `v_(0)` is the speed in truck, frame in ground frame, the velocity is `v_(0)-(5v_(0)//7)=2v_(0)//7` towards the right.
The answer is independent of `M` or `R`.