In the figure, the blocks unequal masses `m_1` and `m_2` (`m_1 lt m_2`).`m_2` has a downward acceleration a. The pulley P has a radius r, and some mass. The string does not slip on the pulley. Find the acceleration of block and angular acceleration of pulley. (I = momentum of inerita of pulley)

Explanation

`T_1 - m_1 g = m_1 a" …(1)`
`m_2 g - T_2 = m_2 g" …(2)"`
Total toreque = `I alpha`
`(T_2 - T_1)P = I alpha " ...(3)`
`a = alpha " ...(4)"`
By. Eq (1), (2) (3) and (4) `rArr`
`a=((m_2 - m_1))/(m_2 + m_1 + I/r^2)g rArr alpha = a/r`