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NEETPhysicsGravitation

Match the hypothetical planets in List-I (with given mass and radius in terms of Earth's mass M and radius R ) with their corresponding escape velocities in List-II (in terms of Earth's escape velocity v_e ). List-I List-II (A) Mass 2M , Radius R 2 (I) v_e (B) Mass M 2 , Radius 2R (II) v_e 2 (C) Mass 2M , Radius 2R (III) 2v_e (D) Mass 4M , Radius R 4 (IV) 4v_e Choose the correct answer from the options given below:

Options

  1. A(A)-(III), (B)-(II), (C)-(I), (D)-(IV)
  2. B(A)-(II), (B)-(III), (C)-(IV), (D)-(I)
  3. C(A)-(IV), (B)-(I), (C)-(II), (D)-(III)
  4. D(A)-(III), (B)-(II), (C)-(IV), (D)-(I)

Correct answer

A. (A)-(III), (B)-(II), (C)-(I), (D)-(IV)

Step-by-step solution

The escape velocity on the surface of a planet of mass M and radius R is given by v = 2GM R . For Earth, v_e = 2GM R . For planet (A): Mass = 2M , Radius = R 2 v_A = 2G(2M) R 2 = 4 2GM R = 2v_e . (Matches III) For planet (B): Mass = M 2 , Radius = 2R v_B = 2G ( M 2 ) 2R = 1 4 2GM R = v_e 2 . (Matches II) For planet (C): Mass = 2M , Radius = 2R v_C = 2G(2M) 2R = 2GM R = v_e . (Matches I) For planet (D): Mass = 4M , Radius = R 4 v_D = 2G(4M) R 4 = 16 2GM R = 4v_e . (Matches IV) Therefore, the correct matching is (A)-

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