The rope shown in figure is wound around a cylinder of mass `4 kg` and moment of inertia `0.02 kgm^2` about the cylinder axis. If the cylinder rolls without slipping, then the linear acceleration of its centre of mass is.
.

Options

A. `6.7ms^(-2)`
B. `10.0ms^(-2)`
C. `9.0ms^(-2)`
D. None of these

Answer

A

Explanation

For rotational motion
`tau=Ialpha`
`impliesF(2R)=3/MR^(2)(a/R)`
`impliesa=(4R)/(3M)=(4(20))/(3(4))=6.7ms^(-2)`