Question

A massless platform is kept on a light elastic spring, as shown in the figure. When particle of mass $0.1kg$ is dropped on the pan from a height of $0.24m$, the particle strikes the is pan, and the spring is compressed by $0.01m$. From what height should the particle be dropped to cause a compression of $0.04m$?

• A. $0.96m$
• B. $2.96m$
• C. $3.96m$
• D. $0.48m$

Answer 1

The correct option is C $3.96m$

Here, $m=0.1kg,h=0.24mx=0.01m$ When stone is dropped from a height h and the spring is compressed by$x$, then loss in P.E. of particle $=mg(h+x)$, while gain in elastic potential energy of spring will be$\frac{1}{2}k{x}^2$

$\therefore mg(h+x)=\frac{1}{2}k{x}^2$

Similarly,

$mg(h^{\prime }+x^{\prime })=\frac{1}{2}kx{{}^{\prime }}^2$

Dividing, we get

$\frac{h+x}{h^{\prime }+x^{\prime }}={\left(\frac{x}{x^{\prime }}\right)}^2$

$\frac{0.24+0.01}{h^{\prime }+x^{\prime }}={\left(\frac{x}{x^{\prime }}\right)}^2$ on solving, we get $h^{\prime }=3.96m$