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

A massless platform is kekpt on a light elastic spring as shown in the

1.	A massless platform is kekpt on a light elastic spring as shown in the figure. When a particle of 0.1kg mass is dropped on the pan from a height of 0.24m, the particle strikes the pan, and the spring compresses by 0.01m. From what height should the particle be dropped to cause a compression of 0.04m?
Answer» Solution :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//2ky^(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`