A string is wrapped on a wheel of moment of inertia 0.20 kg-m^2 and radius 10 cm and goes through a light pulley to support a block of mass 2.0 kg as shown in figure. Find the acceleration of the block.

Explanation

Suppose the monkey accelerate upward with acceleration a and the block accelerates downward with acceleration `a_1`. Let force exerted by monkey is equal to T.
From the free body diagram of monkey
T-mg-ma=0` ……….i
`rarr T=mg+ma`
Again, from the free body diagram of block,
`T+ma_1 -mg=0`
`mg+ma+ma_1-mg=0` (From i. )
`rarr ma=-ma_1`
`rarr a_1 =a`

Acceleration -a downward, i.e. a upward. Teh block and the monkey move in the same direction with equal acceleratiion.
intitially they are at rest (no force is exerted by monkey), motion of monkey of block occurs as they have same weight (same mass). Their separation will not change as the passes.