The weight of a body is less in mines. Why?

OR: The weight of a body is less inside the earth than on the surface. Why?

The weight of a body on the earth’s surface is, \[W=mg\] where, $m$ is the mass of the body and $g$ is the acceleration due to gravity.

The effective acceleration due to gravity at depth $x$ from the surface of earth is, \[g’=\left(1-\frac{x}{R}\right)mg\] where, $R$ is the radius of the earth.

Let $W_x$ be the weight of the body at depth $x$. Then, \[W_x=mg’=m\left(1-\frac{x}{R}\right)g=\left(1-\frac{x}{R}\right)W\]

Since $x<R$, $W_x<W$. So, the weight of the body is less inside the earth than on the surface. That’s why, the weight of a body is less in mines.

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