Two blocks of masses `1 kg` and `3 kg` are moving with velocities `2 m//s` and `1 m//s` , respectively , as shown. If the spring constant is `75 N//m` , the maximum compression of the spring is

Options

A. `5 cm`
B. `2 cm`
C. `3 cm`
D. `4 cm`

Answer

B

Explanation

Due to spring force , velocity of `1 kg` decreases and that of `3 kg` increases . At the maximum compression , both the blocks move with same velocity.
By the momentum conservation
` 1 xx 2 + 3 xx1 = (1 + 3)v rArr v = (5)/(4) m//s`
By the energy conservation
`(1)/(2) 1 (2)^(2) + (1)/(2) xx 3 (1)^(2) = (1)/(2) (1 + 3) v^(2) + (1)/(2) kx^(2)`
`(7)/(2) = 2((5)/(4))^(2) + (75)/( 2) x^(2) rArr (75)/(2) x^(2) = (7)/(2) - (25)/(8) = (3)/(8)`
`x^(2) = (1)/(100) rArr x = (1)/(10) m = 10 cm`