Question

A small block of superdense material has mass $2\times 10^{24}kg$ . It is at a height $h<<R$ . It falls towards the earth. Find its speed when it is at a height $h/2$ .

• A. $\sqrt{\frac{2gh}{3}}$
• B. $\sqrt{\frac{3gh}{4}}$
• C. $\sqrt{\frac{3gh}{5}}$
• D. $\sqrt{\frac{gh}{2}}$

Answer 1

Answer: (B)

Mass of earth is, $M=6\times 10^{24}kg$
Mass of superdense material $m=2\times 10^{24}kg=\frac{M}{3}$
From momentum conservation, $M{V}_1=\frac{M}{3}{V}_2$
From energy conservation $V_1=\frac{V_2}{3}$
$\frac{1}{2}M{V}_1^2+\frac{1}{2}\left(\frac{M}{3}\right)V_2^2=\frac{GM\left(\frac{M}{3}\right)}{\frac{h}{2}+R}-\frac{GM\left(\frac{M}{3}\right)}{h+R}$
$\therefore v_2=\sqrt{\frac{3gh}{4}}$