The system shown in the figure is in equilibrium. Masses `m_(1) & m_(2)` are 2kg and 8 kg respectively. The compression in right spring is 0.5 m. (Both spring have the same natural length) `[K_(1)=20 N//m, K_(2)=70 N//m]`. Choose the correct option(s) :

Options

A. elongation in left spring is 0.5m
B. elongation in left spring is 0.25 m
C. Tension is string is 45 N
D. Just after left spring is cut `m_(1)`, has upward acceleration.

Answer

C, D

Explanation

F = 8t
`m(dv)/(dt) = 8t`
`m underset(0)overset(v)int dv = 8 underset(0) overset(t) int t dt`
`mv = 4t^(2)`
or `m(dx)/(dt) = 4t^(2) implies dx = (4t^(2))/(m) dt = 2t^(2) dt`
`W = intFdx = underset(0)overset(2)int (8t xx 2t^(2)) dt = 64J`