A uniform solid cylinder of mass `2 kg` and radius `0.2 m` is released from rest at the top of a semicircular track of radius `0.7 m` cut in a block of mass `M = 3 kg` as shown in Fig. The block is resting on a smooth horizontal surface and the cylinder rolls down without slipping. Based on the above information, answer the following questions:

The speed of the point of contact of the cylinder with the block w.r.t. ground, when the cylinder reaches the bottom of the track is

Options

A. `2/(sqrt(11))m//s`
B. `8/(sqrt(11))m//s`
C. `4/(sqrt(11))m//s`
D. `6/(sqrt(11))m//s`

Answer

D

Explanation

`mv=Mv_(0)`

`mg(R-r)=1/2mv^(2)+1/2Iomega^(2)+l1/2Mv_(0)^(2)`
`implies v_(0)=4/(sqrt(11))m//s`
`v=6/(sqrt(11)) m//s`