The pulley shown in figure has a radius of 20 cm and moment of inertial 0.2 kg-m^2. The string going over it is attached at one end to a vertical sprign of spring constant 50 N/m fixed from below and supports a 1 kg mas at other end. The system is released from rest with the spring at its natural length. Find the speed of the block when it has desceds through 10 cm. Take `g=10 m/s^2`.

Explanation

`l=0.2kgm^2,r0.2m, kkk=50N/m`
`m=1 k , g=10 ms^2, h=0.1m`
Therefore applying laws of conservatio of energy
`mgh=1/2mv^2+1/2kx^2`

`rarr a=1/2x1xxv^2+1/2xx0.2`
`xxv^2/0.04=(1/2)xx50xx0.01(x=h)`
`rarr 1=0.5v^2+2.5v^2+1/4`
`rarr 3v^2=3/4`
`rarr v^2=1/4`
`rarr v=1/2=0.5m/s`