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7.Gravitation
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Assuming the earth to be a sphere of uniform mass density, how much would a body weigh (in $N$) half way down to the centre of the earth if it weighed $250\; N$ on the surface?
A
$250$
B
$300$
C
$144$
D
$125$
Solution
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, $d=\frac{1}{2} R_{e}$
$g^{\prime}=\left(1-\frac{d}{R_{e}}\right) g$
$=\left(1-\frac{R_{e}}{2 \times R_{e}}\right) g=\frac{1}{2} g$
Weight of the body at depth $d$, $W^{\prime}=m g^{\prime}$
$=m \times \frac{1}{2} g=\frac{1}{2} m g=\frac{1}{2} W$
$=\frac{1}{2} \times 250=125 \;N$
Standard 11
Physics
