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COMEDK · Physics · 9. Gravitation

Two spherical planets \(P\) and \(Q\) have the same uniform density \(\rho\), and masses \(M_P\) and \(M_Q\) and surface areas \(A\) and \(4 A\) respectively. Another spherical planet R also has the same uniform density \(\rho\), and its mass is \(\mathrm{Mp}+\mathrm{MQ}\). The escape velocities from these planets is

  1. A \(V_R=V_Q > V_P\)
  2. B \(V_R < V_Q < V_P\)
  3. C \(V_R > V_Q=V_P\)
  4. D \(V_R > V_Q > V_P\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(V_R > V_Q > V_P\)

Step-by-step Solution

Detailed explanation

The surface area of a sphere is \(A = 4 \pi R^2\). Given \(A_P = A\) and \(A_Q = 4A\), we have \(4 \pi R_P^2 = A\) and \(4 \pi R_Q^2 = 4A\). This implies \(R_Q^2 = 4 R_P^2\), so \(R_Q = 2 R_P\). The mass of a planet with uniform density \(\rho\) is…