A) \[0.5%\] decrease
B) \[2%\] decrease
C) \[0.5%\] increase
D) \[1%\] increase
Correct Answer: A
Solution :
At an altitude h, the acceleration due to gravity is \[g'=g\,\left( 1-\frac{2h}{{{R}_{e}}} \right)\Rightarrow \,mg'=mg\left( 1-\frac{2h}{{{R}_{e}}} \right)\]i.e., \[w'=w\,\left( 1-\frac{2h}{{{R}_{e}}} \right)\] \[\frac{99}{100}w=w\,\left( 1-\frac{2h}{{{R}_{e}}} \right)\,\Rightarrow \] i.e., \[h=0.005\,{{R}_{e}}\] At a point below, the surface of earth at depth h. The weights of body is given by \[w'=w\left( 1-\frac{h}{{{R}_{e}}} \right)\Rightarrow \,\frac{w'}{w}=0.995\]\[%\Delta w=\frac{(1-0.995)}{w}\times 100=0.5%\]
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