JEE Mains · Physics · STD 11 - 7. gravitation
The ratio of escape velocity of a planet to the escape velocity of earth will be:Given : Mass of the planet is \(16\) times mass of earth and radius of the planet is \(4\) times the radius of earth.
- A \(4:1\)
- B \(2:1\)
- C \(1: \sqrt{2}\)
- D \(1: 4\)
Answer & Solution
Correct Answer
(B) \(2:1\)
Step-by-step Solution
Detailed explanation
\(V_{\text {escape }}=\sqrt{\frac{2 G M}{R}}\) \(\therefore V_{\text {escape }} \text { for planet }=\sqrt{\frac{2 G\left(16 M_E\right)}{\left(4 R_E\right)}}=2 \sqrt{\frac{2 G_E}{R_E}}\) \(=2\left(V_{\text {escape }} \text { for Earth }\right)\)
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