Question

Potential energy of a $3kg$ body at the surface of a planet is $54J$ then escape velocity will be.

• A. $18m/s$
• B. $162m/s$
• C. $36m/s$
• D. $6m/s$

Answer 1

Answer: (D)

$6m/s$

Magnitude of gravitational potential energy at surface, $|P.E|=\frac{GMm}{R}$

For $m=3kg$ gives $54=\frac{GM\left(3\right)}{R}$

$⟹\frac{GM}{R}=\frac{54}{3}$

Now escape velocity, $v_e=\sqrt{\frac{2GM}{R}}=\sqrt{\frac{2\times 54}{3}}$

$⟹v_e=6m/s$