A massless platform is kept on a light 0.1 kg 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. (a) `0.96m`
B. (b) `2.96m`
C. (c) `3.96m`
D. (d) `0.48m`

Answer

C

Explanation

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