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Q.

Weight of a body of mass $m$ decreases by $1 %$ when it is raised to height $h$ above the earth's surface. If the body is taken to a depth $h$ in a mine, then in its weight will

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a

decrease by $0.5 %$

b

decrease by $2 %$

c

increase by $0.5 %$

d

increase by $1 %$

answer is A.

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Detailed Solution

$m$ decreased by $1 %$ for height
$g_{h} = g {[1 + \frac{h}{R}]}^{- 2} \frac{∆ g_{h}}{g} = \frac{- 2 h}{R}$
for depth.
$g_{d} = g [1 - \frac{d}{R}] \frac{∆ g_{d}}{g} = \frac{- d}{R} (here d = h) \frac{∆ g_{h}}{g} = \frac{2 ∆ g_{d}}{g} \frac{∆ g_{d}}{g} = \frac{1}{2} \frac{∆ g_{h}}{g}$

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