Question

Why is weight of a body lesser at equator than at poles?

Answer 1

1. Weight of a body at a point depends upon two factors i.e. mass of body and acceleration due to gravity at that point. Since the mass of a body is constant everywhere hence the variation in weight of a body is due to variation in the acceleration due to gravity.
2. The formula of the weight of a body of mass $\text{'}\text{'}\mathrm{m}\text{'}\text{'}$at a point is given by $\mathrm{W}=\mathrm{mg}$ where $\text{'}\text{'}\mathrm{g}\text{'}\text{'}$is the acceleration due to gravity. Since mass is constant therefore $\mathrm{W}\mathrm{\alpha }\mathrm{g}$which means more the value of $\text{'}\text{'}\mathrm{g}\text{'}\text{'}$more will be the weight or vice-versa.
3. Acceleration due to gravity at a place is $\mathrm{g}=\frac{\mathrm{GM}}{{\mathrm{R}}^2}$, where $G$ is gravitational constant, $M$ is the mass of the earth (constant) and $R$ is the radius of the earth.
4. Since the earth is not totally spherical and the radius of the equator is more than the radius at the pole i.e.,${\mathrm{R}}_{\mathrm{e}}>{\mathrm{R}}_{\mathrm{P}}$
5. More the value of radius less will be the value of acceleration due to gravity because the acceleration due to gravity is inversely proportional to the radius.
6. Therefore, ${\mathrm{g}}_{\mathrm{e}}<{\mathrm{g}}_{\mathrm{p}}$.More the value of $\text{'}\text{'}\mathrm{g}\text{'}\text{'}$more will be weight. Thus weight at poles will be greater than weight at equators.

Hence, the weight of a body is lesser at the equator than at the poles