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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 ? (a) d = 3h/2 (b) d = h /2 (c) d = h (d) d = 2 h

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 ?
 
(a) d = 3h/2
(b) d = h /2
(c) d = h
(d) d = 2 h

Grade:6

1 Answers

Deepak Patra
askIITians Faculty 471 Points
6 years ago

(d) Variation of g with altitude is, g­h = g [1-2h/R];

variation of g with depth is, gd = g [1 – d/R]

Equating g and gd , we get d = 2h

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