Question

A planet has mass M and radius R. A small object of mass $m$ is dropped from a distance of 3R from the planet center. The speed of the object is $\sqrt{kGM/R}$ when it hits the surface of the planet. Calculate k.

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{3}{4}$
• D. $\frac{4}{3}$
• E. $\frac{3}{2}$

Answer 1

Answer: (D)

$\frac{4}{3}$

From conservation of energy of the mass,

Gain in kinetic energy=Loss in gravitational potential enerrgy

$⟹\frac{1}{2}m{v}^2=-\frac{GMm}{3R}-(-\frac{GMm}{R})$

$⟹\frac{1}{2}m{v}^2=\frac{2GMm}{3R}$

$⟹v=\sqrt{\frac{4GM}{3R}}$

$⟹k=\frac{4}{3}$