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

Explanation

If the particle is dropped from a height .h. and the spring is compressed by y. Loss in PE of the particle will be mg (h+y) while gain in elastic potential energy is `1//2 ky^(2)`.
According to conservation of mechanical energy
`mg(h+y)=(1)/(2)ky^(2)`
As .m. and .K. remain same
`(h_(1)+y_(1))/(h_(2)+y_(2))=((y_(1))/(y_(2)))^(2)`
`(0.24 + 0.01)/(h_(2)+0.04)=((0.01)/(0.04))^(2),h_(2)=3.96m`