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

Options

A. `0.15 m`
B. `0.12 m`
C. `1.5 m`
D. `0.5 m`

Answer

A

Explanation

By the law of conservation of energy.

i.e., `Delta K + Delta U = 0`
`(0 - (1)/(2) mv^(2)) + ((1)/(2) kx^(2) - 0) = 0`
`(1)/(2) mv^(2) = (1)/(2) kx^(2)`
`implies x^(2) = (mv^(2))/(k)`
`implies x = sqrt(((mv^(2))/(k)))`
`implies sqrt(((0.5 xx 1.5 xx 1.5)/(50)))`
`:. 0.15m`