Question

A small pulley of radius $20cm$ and moment of inertia $0.32kg-m^2$ is used to hang a $2kg$ mass with the help of mass less string. If the block is released, for no slipping condition acceleration of the block will be

• A. $2m/s^2$
• B. $4m/s^2$
• C. $1m/s^2$
• D. $3m/s^2$

Answer 1

The correct option is A $2m/s^2$

For Block
$20-T=2a....\left(i\right)$
For pulley
$TR=I\alpha$ $\therefore T\left(0.2\right)=\left(0.32\right)\alpha$ $T=1.6\alpha ....\left(ii\right)$
$a=R\alpha =0.2\alpha ...\left(iii\right)$
Solving these equations, we get
$a=2m/s^2$