There is a spring with netural length `L_(0)`. Two masses `m_(1)` and `m_(2)` are connected to both of its ends as shown in figure. The whole system is held at rest. At any time `t =0, m_(2)` is released and system starts free fall. Initial stretched length of spring before fall is `L.` what is the displacement of centre of mass as function of time?

Options

A. `g t^(2)`
B. `(1)/(2)g t^(2)`
C. `(g)/(K)t^(2)`
D. `(m_(1)+m_(2))/(m_(1)m_(2))xxt`

Answer

B

Explanation

`a_(cm) = (m_(1)a_(1)+m_(2)a_(2))/(m_(1)+m_(2)), a_(1) =a_(2) = g`
`:. S = (1)/(2) a_(cm)t^(2) = (1)/(2)g t^(2)`