A mass of 2 kg initially at a height of 1.2 m above an uncompressed spring with spring constant `2 xx 10^4` N/m , is released from rest to fall on the spring.
Taking the acceleration due to gravity as `10 m//s^2` and neglecting the air resistance , the compression of the spring in mm is

Options

A. 20
B. 40
C. 50
D. 60

Answer

C

Explanation

Key Idea when a mass m is fall from height h on a uncompressed spring then the maximum compression is given by relation ,
`mgh =1/2 kx^2`
(principle of energy conservation )
Given , mass of body , m= 2kg , height , h= 1.2 m spring constant , `k= 2xx 10^4 N//m` and acceleration due to gravity ` g= 10 m//s^2`
Then `x =sqrt((2mgh)/k) rArr x = sqrt(( 2xx 2 xx 1.2 xx 10)/(2 xx 10^4) )`
`rArr = 4.89 xx 10^(-2) m ~~ 50 mm`