Question

The potential energy of a body of mass $3\text{kg}$ on the surface of a planet is $54\text{J}$ Its escape velocity will be –

• A. $162\text{m/s}$
• B. $36\text{m/s}$
• C. $18\text{m/s}$
• D. $6\text{m/s}$

Answer 1

The correct option is D $6\text{m/s}$

Given :
$m=3\text{kg}$ and $U_i=54\text{J}$

Using law of conservation of energy, $$K_i+U_i=K_f+U_f$$At infinity, $K_f=0$ as well as $U_f=0$

Thus, $K_i=-U_i$

$\Rightarrow \frac{1}{2}m{v_e}^2=-U_i$

Substituting the given data we get,

${v_e}^2=\frac{2\times 54}{3}=36\Rightarrow v_e=6\text{m/s}$

Hence, option (d) is the correct answer.