Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If a body is taken to a depth d = R_E 2 , its weight becomes half of its weight on the surface, but if it is taken to a height h = R_E 2 , its weight becomes less than half. Reason (R): For a given distance from the surface of the Earth, the decrease in the value of acceleration due to gravity is a

Step-by-step solution

Let g be the acceleration due to gravity on the surface of the Earth. At depth d = R_E 2 , the acceleration due to gravity is g_d = g (1 - d R_E ) = g (1 - 1 2 ) = g 2 . Thus, the weight becomes half. At height h = R_E 2 , the acceleration due to gravity is g_h = g ( R_E R_E+h )^2 = g ( R_E R_E + R_E/2 )^2 = g ( 2 3 )^2 = 4g 9 . Since 4 9 The decrease in g at depth d = R_E 2 is g_ in = g - g 2 = g 2 = 0.5g . The decrease in g at height h = R_E 2 is g_ out = g - 4g 9 = 5g 9 0.55g . Since g_ out > g_ in , the decreas