A massless platform is kept 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 0.24 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 ?

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 a particle of 0.1kg 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 ?
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//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`