Question

A small block of superdene material has mass $2\times {10}^{24}$ kg. It isn't at a height $h<<R$. It falls towards earth. Find its speed when it is at a height $h/2$

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

Answer 1

Answer: (B)

$\sqrt{\frac{3gh}{4}}$

$\frac{M}{2}{v}_1^2+\frac{1}{2}\times \frac{M}{3}{v}_2^2$

$=\frac{GM\left(\frac{M}{3}\right)}{(\frac{h}{2}+R)}-\frac{GM\left(\frac{M}{3}\right)}{(h+R)};m{v}_1=\frac{M}{3}{v}_2$
or

$v_2^2\frac{2}{9}=\frac{GMh}{6R_2}$ or $v_2=\sqrt{\frac{3gh}{4}}$.