JEE Mains · Physics · STD 11 - 7. gravitation
The radii of two planets \(A\) and \(B\) are \(R\) and \(4 R\) and their densities are \(\rho\) and \(\rho / 3\) respectively. The ratio of acceleration due to gravity at their surfaces \(\left(g_A: g_B\right)\) will be
- A \(1: 16\)
- B \(3: 16\)
- C \(3: 4\)
- D \(4: 3\)
Answer & Solution
Correct Answer
(C) \(3: 4\)
Step-by-step Solution
Detailed explanation
\(g=\frac{G M}{R^2}=\frac{G}{R^2} \times \rho \times \frac{4 \pi}{3} R^3=\left(\frac{4 \pi}{3} G\right) \rho R\) \(\frac{g_A}{g_B}=\frac{R \times \rho}{4 R \times \frac{\rho}{3}}=\frac{3}{4}\)
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