A pulley with two blocks system is attached to the ceiling of a lift upward with an acceleration `a_(0)` . Find the deformation in the spring.

Explanation

Non-inertial Frame

Let relative to the centre of pulley, `m_(1)` accelerates downward with a and `m_(2)` accelerates upwards with a. Applying Newton's 2nd law.
`m_(1) g +m_(1) a_(0) - T= m_(1) a ` ....(i)
`T - m_(2) g - m_(2) a_(0) =m_(2) a ` ....(ii)
On adding (iv) and (v)we get
`a= ((m_(1) -m_(2))/( m_(1) +m_(2))) (g+ a_(0))` ....(iii)
Substituting a in equation (i)
We get `T = ( 2m_(1) m_(2)(g+ a_(0)))/( m_(1) +m_(2))`
`:.x=(F)/(k) = ( 2T )/( k ) = ( 4 m_(1) m_(2) ( g+ a_(0)))/((m_(1) + m_(2))k)`