Assuming the Earth to be a sphere of uniform | vedclass

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Question

(D) The weight of a body on the surface of the Earth is given by $W = mg = 200 \, N$.The acceleration due to gravity at a depth $d$ below the surface

Vedclass · Accepted Answer

$100$

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(D) The weight of a body on the surface of the Earth is given by $W = mg = 200 \, N$.The acceleration due to gravity at a depth $d$ below the surface of the Earth is given by the formula $g' = g(1 - d/R)$,where $g$ is the acceleration due to gravity at the surface and $R$ is the radius of the Earth.Given the depth $d = R/2$,we substitute this into the formula:$g' = g(1 - (R/2)/R) = g(1 - 1/2) = g/2$.The weight of the body at depth $d$ is $W' = mg' = m(g/2) = (mg)/2$.Since $mg = 200 \, N$,we have $W' = 200/2 = 100 \, N$.

Assuming the Earth to be a sphere of uniform mass density,the weight of a body at a depth $d = R/2$ from the surface of the Earth,if its weight on the surface of the Earth is $200 \, N$,will be $........... \, N$ (Given $R =$ Radius of Earth).

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