AP EAMCET · PHYSICS · Gravitation
The escape velocity of a body from a planet of mass M and radius R is \(14 \mathrm{~km} \mathrm{~s}^{-1}\). The escape velocity of the body from another planet having same mass and diameter 8 R (in \(\mathrm{km} \mathrm{s}^{-1}\) ) is
- A \(7\)
- B \(10.5\)
- C \(14\)
- D \(28\)
Answer & Solution
Correct Answer
(A) \(7\)
Step-by-step Solution
Detailed explanation
\( v_e = \sqrt{\frac{2GM}{R}} \) \( v_e \propto \frac{1}{\sqrt{R}} \) \( \frac{v_{e2}}{v_{e1}} = \sqrt{\frac{R_1}{R_2}} \) \( R_1 = R \), \( R_2 = \frac{8R}{2} = 4R \) \( \frac{v_{e2}}{14 \, \mathrm{km} \, \mathrm{s}^{-1}} = \sqrt{\frac{R}{4R}} = \frac{1}{2} \)…
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