Question

A small block of super dense material has mass 2 × 10²⁴ kg. It is 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. $\sqrt{\frac{3gh}{5}}$
• D. $\sqrt{\frac{gh}{2}}$

Answer 1

Answer: (B)

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

Answer 2

$\frac{M}{2}v_{1}^{2} + \frac{1}{2} \times \frac{M}{3}v_{2}^{2}$

= $\frac{GM\left( \frac{M}{3} \right)}{\left( \frac{h}{2} + R \right)} - \frac{GM\left( \frac{M}{3} \right)}{(h + R)};mv_{1} = \frac{M}{3}v_{2}$

or $v_{2}^{2}\frac{2}{9} = \frac{GMh}{6R_{2}}orv_{2} = \sqrt{\frac{3gh}{4}}$.