Question

A massless platform is kept on a light elastic spring as shown in fig. When a 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

Answer 1

The correct option is C

3.96 m

Let the particle be dropped from a height h an d the spring be compressed by y. According to the conservation of mechanical energy. Loss in PE of the particle = gain in elastic potential energy of the spring.

$Mg(h+y)=\frac{1}{2}k{y}^2$

Now, as the particles and spring are same for second case,

$\frac{h_1+y_1}{h_2+y_2}$ = $(\frac{y_1}{y_2}{)}^2$ or $(\frac{0.24+0.01}{h_2+0.04})$ = $(\frac{0.01}{0.04}{)}^2$

Solving, we get $h_2=3.96m$