question_answer

The change in the value of g at a height h above the surface of the earth is the same as at a depth d below the surface of earth. When both d and h are much smaller than the radius of earth, then which one of the following is correct?                                                                                                                                                           [AIEEE 2005]                

A)  \[d=\frac{h}{2}\]          

B)       \[d=\frac{3h}{2}\]

C)  \[d=2h\]         

D)       \[d=h\]

Correct Answer: C

Solution :

[c] The variation in gravitational acceleration with height and depth from the earth's surface, respectively given by             ... (i) and                     ...(ii) From Eqs. (i) and (ii), we get