A mass of 0.5 kg moving with a velocity of 1.5 m/s on a horizontal smooth surface, collides with a nearly weightless spring of force constant `K=50N//m`. The maximum compression of the spring would be:

Options

A. 0.3 m
B. 1.5 m
C. 0.15 m
D. 0.25 m

Answer

C

Explanation

At the maximum compression,
K.E. of moving mass = P.E stored in spring
`(1)/(2)mv^(2)=(1)/(2)Kx^(2)`
`x^(2)=(mv^(2))/(K)`
`x=(sqrt(mv^(2)))/(K)`
`m=0.5kg, v=1.5m//s, K=50N//m`
Maximum compression
`x=sqrt((0.5xx(1.5)^(2))/(50))`
`=sqrt((5xx15xx15xx10^(-3)xx10^(-1))/(5))`
`=sqrt(15xx15xx10^(-4))`
`=15xx10^(-2)`
`x=0.15m`