MHT CET · Physics · Gravitation
The escape velocity from the surface of earth of mass 'M' and radius 'R' is 'Ve'. The escape velocity from the surface of a planet whose mass and radius are 3 times that of the earth, will be
- A \(\mathrm{q} \mathbf{V}_{\mathrm{e}}\)
- B \(3 \mathrm{Ve}\)
- C \(\mathbf{V} \mathrm{e}\)
- D \(12 \mathrm{Ve}\)
Answer & Solution
Correct Answer
(C) \(\mathbf{V} \mathrm{e}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{V}_{\mathrm{e}}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}\)
\(\mathrm{V}_{\mathrm{e}}^{\prime}=\sqrt{\frac{2 \mathrm{G} \times 3 \mathrm{M}}{3 \mathrm{R}}}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}=\mathrm{V}_{\mathrm{e}}\)
\(\mathrm{V}_{\mathrm{e}}^{\prime}=\sqrt{\frac{2 \mathrm{G} \times 3 \mathrm{M}}{3 \mathrm{R}}}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}=\mathrm{V}_{\mathrm{e}}\)
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