Question

Find the percentage change in the weight of a body when it is taken from equator to poles. The polar radius is 6,357 km and equatorial radius is 6,378 km.

Answer 1

Step 1: Given data:

Polar radius $\left(R_p\right)=6,357km$

Equatorial radius $\left(R_e\right)=6,378km$

Step 2: Formulae for the value of gravitational force at the poles and equator.

At the poles (${\mathrm{g}}_{\mathrm{p}}$) = $\frac{\mathrm{GM}}{{\left({\mathrm{R}}_{\mathrm{p}}\right)}^2}$

At the equator ($g_e$) = $\frac{\mathrm{GM}}{{\left({\mathrm{R}}_e\right)}^2}$

Step 3: Finding the ratio of poles and equator

The ratios are given by $=\frac{g_p}{g_e}={\left(\frac{R_e}{R_p}\right)}^2$

$={\left(\frac{6378}{6357}\right)}^2$

${\mathrm{g}}_{\mathrm{p}}=1.0066{\mathrm{g}}_{\mathrm{e}}$

Step 4: Finding the percentage change in the weight of a body

The Percentage change in weight the body is taken from the equator to the poles,

$=\frac{{\mathrm{mg}}_{\mathrm{p}}-{\mathrm{mg}}_{\mathrm{e}}}{{\mathrm{mg}}_{\mathrm{e}}}\times 100$

$=\frac{1.006{\mathrm{g}}_{\mathrm{e}}-{\mathrm{g}}_{\mathrm{e}}}{{\mathrm{g}}_{\mathrm{e}}}\times 100$

$$\begin{gathered} =0.0066\times 100 \\ =0.66\% \\ =0.7\% \end{gathered}$$

Therefore, the percentage change in weight the body is $0.7\%$