Question

A body weighs $500N$ on the surface of the earth. How much would it weigh half-way below the surface of the earth?
(A) $125N$
(B) $250N$
(C) $500N$
(D) $1000N$

Answer 1

Hint: In order to solve this question, we should know that mass of the body doesn’t change with the height from the surface of the earth but the acceleration due to gravity changes and thus change in weight appears, here half below the surface of the earth is half of the radius of the earth.

Formula used:
If g is the acceleration due to gravity on the surface of the earth, R is the radius of the earth and h is the height below the surface of the earth then, acceleration due to gravity at this height g’ is given by $g' = g(1 - \dfrac{h}{R})$
The weight of a body of mass m is given by $W = mg$

Complete answer:
We have given that weight of a body at the surface of the earth is $W = 500N$

Now, acceleration due to gravity at half distance from the surface of the earth which means $h = \dfrac{R}{2}$ is given by the formula $g' = g(1 - \dfrac{h}{R})$on putting the value we get,
$
  g' = g(1 - \dfrac{R}{{2R}}) \\
  g' = \dfrac{g}{2} \to (i) \\
 $

On multiplying the equation (i) by the mass of the body m we get,
$mg' = m\dfrac{g}{2} \to (ii)$ now, since weight of a body is given by $W = mg$

So at the height of $h = \dfrac{R}{2}$ below the surface of the earth the weight of the body will by $W' = mg'$ and original weight a the surface of the earth is given to us $W = mg = 500N$, On putting these values in equation (ii) we get,
$
  W' = \dfrac{W}{2} \\
  W' = \dfrac{{500}}{2} \\
  W' = 250N \\
 $
So, the weight of the body at half below the surface of the earth is $250N$

Hence, the correct option is (B) $250N$

Note:It should be remembered that mass is the inherent property of matter whereas weight is the actual force acting on the body due to acceleration due to gravity and weight changes with places whereas mass remains constant as long as there is no relativistic effect on the body.