Question

Derive an expression for the acceleration due to gravity on the suraface of the earth how does weight of an abject change as the object moves from equator to pole of the earth?

Answer 1

To calculate the value of g, we should put the values of G, M and R

Where G=universal gravitational constant, $G=6.7\times {10}^{–11}N{m}^2{kg}^{-2}$

mass of the earth, $M=6\times {10}^{24}kg$,

and radius of the earth, $R=6.4\times {10}^{6}m$.

$g=\frac{GM}{R^2}$

$g=\frac{6.67\times {10}^{-11}\times 6\times {10}^{24}}{(6\times {10}^6{)}^2}=9.8m/s^2$

Thus, the value of acceleration due to gravity of the earth, $g=9.8m/s^2$

Also we know Weight in nothing but the force exerted by the earth with a value of acceleration $=9.8m/s^2$

Now at the poles the value of acceleration due to gravity is higher as compared to the equator as the constant value of

g depends on the radius of the earth which decreases when we come down from poles to the equator.