A massless platform is kept on a light elastic spring, as shown in the figure. When particle of mass 0.1 kg is dropped on the pan from a height of 0.24 m, the particle strikes the pan, and the spring is compressed by 0.01 m. From what height should the particle be dropped to cause a compression of 0.04 m?

Options

A. 0.96 m
B. 2.96 m
C. 3.96 m
D. 0.48 m

Answer

C

Explanation

Let the particle be dropped from a height h and the spring be compressed by y. According to conservation of mechanical energy.
Loss in potential energy of the particle = gain in elastic energy of the spring
`:. mg (h + y) = 1/2 ky^2`
Now, as the particle and spring remain same, hence,
`(h_1 + y_1)/(h_2 + y_2) = ((y_1)/(y_2))^(2) implies ((0.24 + 0.01)/(h_2 + 0.04)) = ((0.01)/(0.04))^(2)`
Solving we get, `h_2 = 3.96 m`.