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 ?

Question

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) 0.96 m (B) 2.96 m (C) 3.96 m (D) 0.48 m

Tardigrade Admin · Accepted Answer

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

∴ m g (h + y) = \frac{1}{2} k y^{2}

Now, as the particle and spring remain same, hence

\frac{h _{1} + y _{1}}{h _{2} + y _{2}} = (\frac{y _{1}}{y _{2}})^{2}

\Rightarrow (\frac{0.24 + 0.01}{h _{2} + 0.04}) = (\frac{0.01}{0.04})^{2}

Solving we get,

h_{2} = 3.96 m