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 sticks to 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?

Step-by-step 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 potential energy of the spring ∴ mg h ⁡ + y = 1 2 k y 2 Now, as the particle and spring remain same, hence h ⁡ 1 + y 1 h ⁡ 2 + y 2 = y 1 y 2 2 0 · 2 4 + 0 · 0 1 h ⁡ 2 + 0 · 0 4 = 0 · 0 1 0 · 0 4 2 Solving we get, h 2 = 3.96 m