Q 11-07-141JEE MainJEE Main 2021 (24 Feb, Shift 2)Medium
A body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator?
[Use $g = \dfrac{GM}{R^2} = 9.8\ \text{m s}^{-2}$ and radius of earth, $R = 6400$ km.]
Answer: (B) 48.83 N
At the pole there is no rotation effect, so $m = \dfrac{49}{9.8} = 5$ kg.
At the equator $g' = g - \omega^2R$ with $\omega = \dfrac{2\pi}{86400} = 7.27\times10^{-5}$ rad/s:
$$\omega^2R = (7.27\times10^{-5})^2\times6.4\times10^6 \approx 0.0338\ \text{m s}^{-2}$$
$$W' = 5(9.8 - 0.0338) \approx 49 - 0.17 = 48.83\ \text{N}$$
Solution by Sreeraj P, M.Sc Physics