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

Options

A. `2m//s^(2)`
B. `4m//s^(2)`
C. `1m//s^(2)`
D. `3m//s^(2)`

Answer

A

Explanation

`20-T=2a` ..(i)
For pulley
`TR=Ialpha`
`thereforeT(0.2)=(0.32)alpha`
`T=1.6alpha` ..(ii)
`a=Ralpha=0.2alpha` ..(iii)
solving these equation we get
`a=2m//s^(2)`