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MHT CET · Physics · Gravitation

Two planets A and B have densities \({ }^{\prime} \varrho_1^{\prime},{ }^{\prime} \varrho_2^{\prime}\) and have radii \({ }^{\prime} \mathrm{r}_1^{\prime},{ }^{\prime} \mathrm{r}_2^{\prime}\) respectively. The ratio of acceleration due to gravity on \(A\) to that of \(B\) is

  1. A \(r_1: r_2\)
  2. B \(r_1 \varrho_1: r_2 \varrho_2\)
  3. C \(r_1^2 \varrho_1: r_2^2 \varrho_2\)
  4. D \(r_1 \varrho_2: r_2 \varrho_1\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(r_1 \varrho_1: r_2 \varrho_2\)

Step-by-step Solution

Detailed explanation

\(g = \frac{GM}{R^2} = \frac{G(\rho \frac{4}{3}\pi R^3)}{R^2} = \frac{4}{3}\pi G \rho R\) \(\frac{g_A}{g_B} = \frac{\frac{4}{3}\pi G \rho_1 r_1}{\frac{4}{3}\pi G \rho_2 r_2} = \frac{\rho_1 r_1}{\rho_2 r_2}\)