Question 384: Gravitation

Question

The escape velocity for earth is $$v$$. A planet having 9 times mass that of earth and radius, 16 times that of earth, has the escape velocity of:

Accepted Answer

Escape velocity of object from planet is given by
$$\begin{aligned}
& \left(v_eight)_p=\sqrt{\frac{2 G M_p}{R_p}} \
& 	herefore \quad\left(v_eight)_p \propto \sqrt{\frac{M_p}{R_p}}
\end{aligned}$$
Now, $$M_p=9 M_e$$ and $$R_ho=16 R_e$$ (given)
$$\begin{aligned}
& \frac{\left(v_eight)_p}{\left(v_eight)_e}=\sqrt{\frac{M_p}{R_p} 	imes \frac{R_e}{M_e}}=\sqrt{\frac{9 M_e}{16 R_e} 	imes \frac{R_e}{M_e}}=\sqrt{\frac{9}{16}}=\frac{3}{4} \
& \Rightarrow \quad\left(v_eight)_p=\frac{3}{4} v
\end{aligned}$$

Answer

$$\frac{v}{3}$$

Answer

$$\frac{2 v}{3}$$

Answer

$$\frac{3 v}{4}$$

Answer

$$\frac{9 v}{4}$$

Gravitation

The escape velocity for earth is $v$. A planet having 9 times mass that of earth and radius, 16 times that of earth, has the escape velocity of:

Choose the correct answer: