Question

Where will you weight more : at the equator or at the poles ?

Answer 1

I will weigh more at poles and weigh less at the equator since weight is the amount of force with which an object is pulled towards the centre of earth.
$$ W = m \times g $$ ........... 1

Where, $$W$$ = Weight

$$m$$ = mass

$$g$$ = Acceleration due to gravity

Since, mass is constant all the time, so,

$$ W \propto g $$ ........2

And we also know that ,

$$ g = G \dfrac{M}{R^2} $$

Where, $$G$$ = Gravitational Constant

$$R$$ = Radius of earth

$$M$$ = Mass of earth

So, $$ g \propto \dfrac{1}{R^2} $$ .......... 3

From equations $$2$$ and $$3$$ , we get ,

$$ W \propto \dfrac{1}{R^2} $$

Since $$R$$ is minimum at poles , and weight is maximum at poles and similarly since $$R$$ is maximum at equator, so weight is minimum at equator.

Hence, we weigh more at poles than at equator