Initially spring is in natural length and block of mass m is released from rest what should be the minimum value of M (in kg) to just move the 2kg block. If this minimum value is `(x)/(8)`kg. Find x

Answer

6

Explanation

With respect to free end, velocity of block is 3 m/s leftward. In position of maximum extension, the block will stop w.r.t. free end. As observed from free end, which is inertial frame `(1)/(2)kx^(2)=(1)/(2)mv^(2)`
`x=sqrt((mv^(2))/(k))=3sqrt((m)/(k))=3sqrt((1)/(10^(4)))=3xx10^(-2)` meter = 3 cm