TS EAMCET · Physics · Gravitation
The ratio of the radii of a planet and the earth is \(1: 2\), the ratio of their mean densities is \(4: 1\). If the acceleration due to gravity on the surface of the earth is \(9.8 \mathrm{~ms}^{-2}\), then the acceleration due to gravity on the surface of the planet is
- A \(4.9 \mathrm{~ms}^{-2}\)
- B \(8.9 \mathrm{~ms}^{-2}\)
- C \(29.4 \mathrm{~ms}^{-2}\)
- D \(19.6 \mathrm{~ms}^{-2}\)
Answer & Solution
Correct Answer
(D) \(19.6 \mathrm{~ms}^{-2}\)
Step-by-step Solution
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Momentum before collision,
\(
p_1=4 m v_1-2 m v_2
\)
Momentum after collision,
\(
p_2=6 m\left(-5 v_2\right)=-30 m v_2
\)
Conservation of momentum gives,
\(
\begin{gathered}
p_1=p_2 \\
\Rightarrow \quad 4 m v_1-2 m v_2=-30 m v_2 \quad \Rightarrow 4 v_1=-32 v_2 \\
\Rightarrow \quad \frac{v_1}{v_2}=\frac{-32}{4}=-8 \text { or }\left|\frac{v_1}{v_2}\right|=8
\end{gathered}
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