Question

The weight of an object in a coal mine, at sea level, and at top of moutain are $W_1,W_2$ and $W_3$ respectively, then

• A. $W_1<W_2>W_3$
• B. $W_1=W_2=W_3$
• C. $W_1<W_2<W_3$
• D. $W_1>W_2>W_3$

Answer 1

The correct option is A $W_1<W_2>W_3$

Weight of the object at a point

$W=m{g}^{\prime }$

where, $g^{\prime }$ is the acceleration due to gravity at a point

And we know that variation in $g$ with height $h$ and depth $d$ from earth surface is given by

At depth $d$, $g^{\prime }=g(1-\frac{d}{R})$

At height $h$, $g^{\prime }=g(1-\frac{2h}{R})$

At sea level, $g^{\prime }=g$

From the above expression, we can say that for any value of $d$ and $h$, $g$ will be maximum at surface or sea level.

So, acceleration due to gravity at sea level is greater than both in a coal mine and at the top of a mountain. But due to lack of data, we can’t compare $W_1$ and $W_3.$

Hence, option $\left(a\right)$ is the correct option.

Why this question ? To make students understand that both with depth and height the acceleration due to gravity decreases.