Question

A body weighs $98N$ on a spring balance at the north pole. What will be the reading on the same scale if it is shifted to the equator? Use $g=$$GM/R^2=9.8m/s^2$ and $R_{earth}$ = 6400 km.

• A. $100N$
• B. $97.66N$
• C. $86.4N$
• D. $75N$

Answer 1

Answer: (B)

$97.66N$

Answer is B.
At poles, the apparent weight is same as the true weight.
Thus, $98N=mg=m$ ($9.8m/s^2$) (as given)
At the equator, the apparent weight is
$m{g}^{\prime }=mg-m{\omega }^{2}R$
The radius of the earth is $6400$ km and the angular speed is
$\omega =\frac{2\pi rad}{24\times 60\times 60s}=7.27\times {10}^{-6}rad/s$
$m{g}^{\prime }=98N-\left(10kg\right){\left(7.27{10}^{-5}{s}^{-1}\right)}^2\left(6400km\right)$
$=97.66N$.
Hence, the reading on the same scale if it is shifted to the equator is $97.66$ N.