The weight of a body of mass m decreases by 1 | vedclass

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(B) The change in acceleration due to gravity at height $h$ is given by $\frac{\Delta g_h}{g} \approx \frac{2h}{R}$.Given that the weight decreases by

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$0.5\%$ decrease

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(B) The change in acceleration due to gravity at height $h$ is given by $\frac{\Delta g_h}{g} \approx \frac{2h}{R}$.Given that the weight decreases by $1\%$,we have $\frac{2h}{R} 	imes 100\% = 1\%$,which implies $\frac{h}{R} = 0.005$.At a depth $d = h$,the change in acceleration due to gravity is given by $\frac{\Delta g_d}{g} = \frac{d}{R} = \frac{h}{R}$.Substituting the value of $\frac{h}{R}$,we get $\frac{\Delta g_d}{g} = 0.005$.Therefore,the percentage decrease in weight at depth $h$ is $0.005 	imes 100\% = 0.5\%$.

The weight of a body of mass $m$ decreases by $1\%$ when it is taken to a height $h$ above the surface of the Earth. What is the percentage decrease in its weight when it is taken to a depth $h$ below the surface of the Earth?

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