String going over a pulley connects two blocks of masses m, and my. String and pulley are light. Calculate acceleration of centre of mass of blocks system.

Explanation

We can apply Newton.s laws of motion to find acceleration of blocks. Let me is moving down with acceleration a then my must be moving up with the same acceleration. Acceleration can be written as follows:
`a=((m_(2)-m_(1))/(m_(1)+m_(2)))g`
Let us assume downward direction as the positive direction then acceleration of centre of mass of blocks can be written as follows:
`a_(cm)=(m_(2)a-m_(1)a)/(m_(1)+m_(2))=((m_(2)-m_(1))/(m_(1)+m_(2)))a`
Substituting value of a, we can write as follows:
`a_(cm)=((m_(2)-m_(1))/(m_(1)+m_(2)))xx((m_(2)-m_(1))/(m_(1)+m_(2)))g`
`rArr a_(cm)=((m_(2)-m_(1))/(m_(1)+m_(2)))^(2)g`