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  • Assuming the Earth to be a sphere of uniform density, how much would a body weigh one fourth down to the centre of the Earth, if it weighed 250 N on the surface?

Assuming the Earth to be a sphere of uniform density, how much would a body weigh one fourth down to the centre of the Earth, if it weighed 250 N on the surface?

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Weight of a body of mass m at the Earth's surface, W=m g=250 N
Body of mass m is located at depth,  d=\frac{R}{4}
Acceleration due to gravity at depth g(d) is given by the relation:

\begin{aligned} g^{\prime} &=\left(1-\frac{d}{R_{e}}\right) g \\ g^{\prime} &=\left(1-\frac{R_{e}}{4 R_{e}}\right) g \\ &g^{\prime}=\frac{3}{4}g \end{aligned}
Weight of the body at depth d 
\begin{aligned} W^{\prime} &=m g^{\prime} \\ &= \frac{3mg}{4}= \frac{3W}{4} \\ &=187.5 \ N \end{aligned}

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avinash.dongre

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