Q 11-07-167JEE MainJEE Main 2020 (7 Jan, Shift 2)Medium
A box weighs $196$ N on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take $g = 10\ \text{m s}^{-2}$ at the north pole and the radius of the earth $= 6400$ km):
Answer: (D) $195.32$ N
Mass $m = \dfrac{196}{10} = 19.6$ kg.
At the equator the balance reading is reduced by $m\omega^2R$, with $\omega = \dfrac{2\pi}{86400} \approx 7.27\times10^{-5}$ rad/s:
$$m\omega^2R = 19.6\times(7.27\times10^{-5})^2\times6.4\times10^6 \approx 0.66\ \text{N}$$
$$W_{eq} \approx 196 - 0.66 \approx 195.3\ \text{N}$$
Solution by Sreeraj P, M.Sc Physics