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Model Paper 6 — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsModel Paper 62 Marks
Question
If earth has a mass 9 times and radius twice that of a planet Mars, calculate the minimum velocity required by a rocket to pull out of the gravitational force of Mars. Take the escape velocity on the surface of earth to be 11.2 $kms ^{-1}$.
✓

Answer

Here, $M_e=9 M_m$, and $R_e=2 R_m$
$v _{ e }$ (escape speed on surface of Earth) $=11.2 km / s$
Let $V_m$ be the speed required to pull out of the gravitational force of mars.
We know that
$
v_{e}=\sqrt{\frac{2 G M_e}{R_e}} \text { and } v_m=\sqrt{\frac{2 G M_m}{R_m}}
$
Dividing, we get $\frac{v_m}{v_e}=\sqrt{\frac{2 G M_m}{R_m} \times \frac{R_e}{2 G M_e}}$
$
\begin{aligned}
& =\sqrt{\frac{M_m}{M_e} \times \frac{R_e}{R_m}}=\sqrt{\frac{1}{9} \times 2}=\frac{\sqrt{2}}{3} \\
& \Rightarrow v_m=\frac{\sqrt{2}}{3}(11.2 km / s)=5.3 km / s
\end{aligned}
$

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