Given radius of earth along the equator is 6378 km and that along the poles is 6357 km. Calculate the percentage change in the weight of a man when he moves from the equator to the poles.

Open in App

Solution

The value of acceleration due to gravity at equator ( $g_{E}$ ) and that at poles ( $g_{p}$ ) are given by

( $g_{E}$ ) = $\frac{G M}{{R^{2}}_{E}}$ and ( $g_{p}$ ) = $\frac{G M}{{R^{2}}_{p}}$

Weight of a person at equator, $W_{E}$ = m( $g_{E}$ )

Weight of the man at pole, $W_{p}$ = m( $g_{p}$ )

The percentage change in the weight of the person in moving from equator to pole = $\frac{W_{p} - W_{E}}{W_{E}}$ * 100

or percentage change = $\frac{m (g_{p}) - m (g_{E})}{m (g_{E})}$ * 100

= $\frac{(g_{p}) - (g_{E})}{(g_{E})}$ * 100

= $\frac{\frac{G M}{{R^{2}}_{p}} - \frac{G M}{{R^{2}}_{E}}}{\frac{G M}{{R^{2}}_{E}}}$ * 100

= $\frac{{R^{2}}_{E} - {R^{2}}_{p}}{{R^{2}}_{p}}$ * 100

= $\frac{{(6378)}^{2} - {(6357)}^{2}}{{(6357)}^{2}}$ * 100

= $\frac{12735 * 21}{6357 * 6357}$ * 100 = 0.66%

Suggest Corrections

Similar questions

g

600 N

A man weighs 600 N on the equator, but when he moves to the pole he finds a slight increase in his weight. This is because:

A man weighs 600N on the equator, but when he moves to the pole he finds a slight increase in his weight. This is because

A man weighs $600 N$ on the equator, but when he moves to the pole he finds a slight increase in his weight. This is because:

Join BYJU'S Learning Program