Match List-I with List-II regarding the acceleration due to gravity ( g ) at various positions relative to the earth's surface ( R is the radius of the earth). List-I List-II P. At a height h = R 1. g/9 Q. At a height h = 2R 2. 0 R. At a depth d = R/2 3. g/4 S. At a depth d = R 4. g/2 Choose the correct answer from the options given below:

Step-by-step solution

The acceleration due to gravity at a height h is given by g_h = g (1 + h R )^2 . For P ( h = R ): g_h = g (1 + 1 )^2 = g 4 (Matches with 3) For Q ( h = 2R ): g_h = g (1 + 2 )^2 = g 9 (Matches with 1) The acceleration due to gravity at a depth d is given by g_d = g (1 - d R ) . For R ( d = R 2 ): g_d = g (1 - 1 2 ) = g 2 (Matches with 4) For S ( d = R ): g_d = g (1 - 1 ) = 0 (Matches with 2) The correct matching is P-3, Q-1, R-4, S-2. Answer: P-3, Q-1, R-4, S-2