A smooth curved surface of height 10 m is ended horizontally. A spring of force constant 200 `Nm^(-1)` is fixed at the horizontal end as shown in figure when an object of mass 10g is released from the top, it travels along the curved path and collides with the spring. Then, the maximum compression in the spring is (Take, `g = 10ms^(-2)`)

Options

A. 10m
B. 0.1 cm
C. 1 m
D. 0.01 m

Answer

B

Explanation

Let spring be compressed upto a compression x then, from energy conservation, mgh = `1/2kx^(2)`
`10 xx 10^(-3) xx 10 xx 10 = 1/2 xx 200 xx x^(2)`
`rArr x^(2) = 10 xx 10^(-3) = 10^(-2)`
`rArr x = sqrt(1/10) = 1/10m = 0.1m`
Thus, compression in the spring is 0.1m