The figure shows a smooth curved track terminating in a smooth horizontal part. A spring of spring constant `400(N)//(m)` is attached at one end to a wedge fixed rigidly with the horizontal part . A 40 g mass is released from rest at a height of 5 m on the curved track. The maximum compression of the spring will be

Options

A. 9.8 m
B. 9.8cm
C. 0.98 m
D. 0.009 km

Answer

B

Explanation

Applying the conservation of momentum to the system.
`mgh = 1/2kx^(2)`
Given, m = 0.04 kg, h=5m, k= 400Nm^(-1)`
and x = deformation (compression in the spring)`
`rArr x=(sqrt(2mgh)/k) = (sqrt(2 xx 0.04 xx 10 xx 5))/400`
`=1/10 m = 10cm ~~ 9.8 cm`