Planet mass radius increases |MotionStraighLineJEEMAIN2023

JEE MAIN 2023

13-4-2023

Question

Given below are two statements :
Statement I: For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases.
Statement II: Escape velocity is independent of the radius of the planet.
In the light of above statements, choose the most appropriate answer from the options given below.

Select the correct option:

Both Statement I and Statement II are incorrect

Statement I is correct but statement II is incorrect

Statement I is incorrect but statement II is correct

Both Statement I and Statement II are correct

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Sol. $$ \begin{aligned} & V_e=\sqrt{\frac{2 G M}{R}} \Rightarrow V_e \propto \sqrt{\frac{M}{R}} \\ & \text { As } \frac{M}{R} \text { increases } \Rightarrow V_e \text { increases } \end{aligned} $$ Statement (1) is correct Also $\mathrm{V}_{\mathrm{e}} \propto \frac{1}{\sqrt{\mathrm{R}}}$ As $\mathrm{V}_{\mathrm{e}}$ depends upon R ⇒ Statement (2) is incorrect Option (2) is correct

Question Tags

JEE Main

Physics

Medium

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