Question

A man weighs $880N$ at the equator.
(A) Calculate his mass(use $g=10m/{{s}^{2}}$ )
(B) How will his weight change if taken to the poles?

Answer 1

Hint Gravitational force is defined as the force between two objects that possess mass. It is a force so it can also be defined as mass times the acceleration with which the mass moves. Gravitational force will vary with distance. The distance of the core of the earth to the poles and the equator will vary.

Complete Step by step answer
Gravitational force is the force that attracts two bodies of masses. The strength of this force will depend on the mass of the bodies as well as the distance of separation of both these bodies. Gravitational force is given by
$F=-\dfrac{GMm}{{{R}^{2}}}$
Here, $M$ is the mass of the first body, $m$ is the mass of the second body, $R$ is the distance of separation between the two bodies, and $G$ is the universal gravitational constant.
By Newton’s second law, force is defined as mass times the acceleration. That is
$F=ma$
Here, if we take the force to be the gravitational force, then the acceleration will be the acceleration due to gravity which is the acceleration with which objects are attracted towards the earth.
$\Rightarrow F=mg$
Here $g=10m/{{s}^{2}}$ .
In the question, it is given that a man weighs $880N$ at the equator. That is, the force is $880N$ . Substituting this value and the value of acceleration due to gravity into the equation for force defined by Newton, we get
$880=m\times 10$
$\Rightarrow m=88kg$
That is, the mass of the man is $88kg$ .
Earth is not perfectly spherical in shape. It is a bit wider at the equator compared to the poles. This means that a person at the equator will be farther away from the core of the earth when compared to a man at the poles. Referring to the gravitational force equation, we now know that the man will weigh more at the poles when compared to a man at the equator.

Hence, the weight of the man will increase if he moves to the poles.

Note
The acceleration due to gravity at the equator is given as $9.78m/{{s}^{2}}$ approximately, whereas the acceleration due to gravity at the poles is given as $9.83m/{{s}^{2}}$ . So the weight change due to the position of the man at the equator and the poles can also be calculated using these values.