Question

Figure shows a uniform smooth solid cylinder `A` of radius `4 m` rolling without slipping on the `8 kg` plank which, in turn, is supported by a fixed smooth surface. Block `B` is known to accelerate down with `6 m//s^(2)` and block `C` moves down with acceleration `2 m//s^(2)`.

If unwrapped length of the thread between the cylinder and block `B` is `20 m` at the beginning, when the system was released from rest, what would it be `2 s` later
A. `28m`
B. `30m`
C. `22m`
D. `32.5m`

Answer 1

Correct Answer - A
The acceleration of the top part of the cylinder (thread) with respect to `CM` of the cylinder is
`a_(AO)=alphaR=1xx4=4m//s^(2)`
Length of the thread `=20+1/2(Ralpha)t^(2)=28m`