The pulleys in figure are identical, each having a radius R and moment of inertia I. Find the acceleration of the block M.

Answer

A, B

Explanation

A is light pulley and B is the descending puley having I=0.20 kg-m^2 and r=0.2 m
Mass of the block =1kg
According to the question
`T_1=m_1a`……….1
`(T_2-T_1)r=Ialpha`……2
`m_2g=m_2alpha a/2=T_1+T_2`……. 3
`T_2-T_1=(Ia)/(2r^2)=(5a)/2`
and `T_1=a` (because `alpha=a/(2r))`
`rarr T_2=/2a`

`rarr m_2g=m_2a/2+7/5a+a`
[using 3]
`rarr (2I)/r^2g=(2I)/r^2a/2+9/2as (1/2mr^2=I)`
`rarr 98.5a+4.5a`
`rarr a=98/9.5=10.3 m/s^2`