Physics - Gravitation Question with Solution | TestHub

The weight of an object is given by $W=mg$, where $g$ is the acceleration due to gravity.

At sea level (surface of the Earth), the acceleration due to gravity is maximum. Let this be $g$.
Thus, the weight at sea level is $W_2=mg$.

In a coal mine of depth $h_1$, the acceleration due to gravity decreases and is given by $g_1=g\left(1-\frac{h_1}{R}\right)$.
Since $g_1<g$, the weight $W_1=m{g}_1<W_2$.

At the top of a mountain of height $h_3$, the acceleration due to gravity also decreases and is given by $g_3=g{\left(\frac{R}{R+h_3}\right)}^2$.
Since $g_3<g$, the weight $W_3=m{g}_3<W_2$.

Therefore, the weight is maximum at sea level, meaning $W_2$ is greater than both $W_1$ and $W_3$. This gives the relation $W_1<W_2>W_3$.

Answer: ${\mathrm{W}}_1<{\mathrm{W}}_2>{\mathrm{W}}_3$