Question

A system consists of two identical cubes, each of mass `3kg`, linked together by a compressed weightless spring of force constant `1000Nm^-1`. The cubes are also connected by a thread which is burnt at a certain moment. At what minimum value of initial compression `x_0` (in cm) of the spring will the lower cube bounce up after the thread is burnt together?

Answer 1

Correct Answer - `(9)`
Let x be the elongation in the spring when it returns back.
`1/2kx_0^2=1/2kx^2+mg(x+x_0)`
On solving, we get
`kx=-mg+-(mg-kx_0)=-2mg+kx_0`
(ignoring negative sign) (i)
And also lower block will bounce up if
`kxgemgimplies-2mg+kx_0gemg`
So `x_0=(3mg)/(k)impliesx_0=9cm`