Question

During motion of a man from equator to pole of earth, its weight will (neglect the effect of change in the radius of earth)

• A. Increase by 0.34%
• B. Decease by 0.34%
• C. increase by 0.52%
• D. Decease by 0.52%

Answer 1

The correct option is A Increase by 0.34%

The correct option is A.

Let the radius at the equator $R_e=6378000m$

Let the radius at the pole $R_p=6356000$

Mass of the earth is$M_e=5.972\times {10}^{24}$

$G=6.67\times {10}^{-11}{m}^{3}k{g}^{-1}{s}^{-2}$

So,

$G{M}_e=5.972\times 6.67\times {10}^{13}$

$=3.985\times {10}^{14}$

$g_e=\frac{G{M}_e}{R_e^2}=\frac{3.985\times {10}^{14}}{4.067\times {10}^{13}}$

$=9.864m/s^2$

$g_p=\frac{G{M}_e}{R_p^2}=\frac{3.985\times {10}^{14}}{4.039\times {10}^{13}}$

$=9.864m/s^2$

Therefore, $\%$ change in the weight is:

$\frac{9.864-9.7965}{9.8692}\times 100$

$=0.68\%$

Thus the weight at the pole increased by $0.34\%$