Question

A frame of mass 200 g when suspended from a masselss spring extends is by 10 cm . A lump of clay of mass 200 g is dropped from rest on to the frame through which pan moves downward?

Answer 1

The condition of clay with pan is inealstic, so energy will not be conserved but momentum will be conserved

Applying law of conservation of momentum

$400V=200\sqrt{2gh}$ or $v=\frac{\sqrt{2gh}}{2}$

KE of putty and pan $=\frac{1}{2}\times 400\times \frac{2gh}{4}=100gh=100\times 30\times g=3000g$

Loss gravitational potential energy $=400gx$

Gain of elastic potential energy

$=\frac{1}{2}\times \frac{200g}{10}[{(10+x)}^2-{10}^2]$

Equating energies

$10g(20+x)\left(x\right)=3000g+400gx$

$20x+x^2=300+40x$

$\Rightarrow$ $x^2-20x-300=0$

$(x-30)(x+10)=0$

$\therefore$ $x=30$ and $-10$

$\therefore$ $x=30$