weight of a body decreases by 1.5%, when it is raised to a height h above the surface of earth. when the same body is taken to same depth h in a mine, its weeight will show
a 0.75% increase
b 0.75% decrease
c 3.0% decrease
d 1.5% decrease
the variation of g with height is given as
g' = g(1 - 2h/R)
so in terms of weight of an object (multiplying both sides by mass 'm')
W' = W(1 - 2h/R)
now as weight reduced by .15%
the new weight will be given a
W' = 0.985W
so,
0.985W = W(1 - 2h/R)
or
0.0985 = (1 - 2h/R)
or
2h/R = 1 - 0.985
or
h = (0.015xR) / 2
thus, the height will be
h = (0.015 x 6.4 x 106) / 2
thus,
h = 48000 m
now,
the variation of g wit depth will be
g' = g(1- d/R)
here d = h = 48000m
or
W' = W(1 - d/R)
or
W' = W[1 - (48000 / 6.4x106)]
or
W' = 0.9925W
thus, the weight will be reduced by
[(W - W') / W] X 100 = 0.0075 x 100
thus,
decrease in weight = 0.75 %
so, the correct answer is option (b).