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?

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

1.	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?
Answer» 0.96 m 2.96 m 3.96 m 0.48 m Solution :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`.