AP EAMCET · PHYSICS · Gravitation
The escape velocity of an object from a planet is \(16 \mathrm{kms}^{-1}\). If the escape velocity of the object from another planet having twice the density and three times the radius of the planet is \(v \sqrt{2} \mathrm{~ms}^{-1}\), then the value of \(v\) is
- A \(12\)
- B \(48\)
- C \(18\)
- D \(36\)
Answer & Solution
Correct Answer
(B) \(48\)
Step-by-step Solution
Detailed explanation
Escape speed is given by \(\begin{aligned} v & =\sqrt{\frac{2 G M}{R}} \\ & =\sqrt{\frac{2 G \times \frac{4}{3} \pi R^3 \times d}{R}}=\quad(\because M=d \times V) .\end{aligned}\) \(\Rightarrow \quad v=\sqrt{\frac{8}{3} G \pi R^2 d}\) Now given for a planet (lets say \(A\) )…
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