Question

A box weighs$196N$ 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 $g=10m/s^2$ at the North Pole and radius of the Earth $R_e=6400km$)

• A. $194.32N$
• B. $194.66N$
• C. $195.34N$
• D. $195.66N$

Answer 1

The correct option is C

$195.34N$

Step 1. Given Data:

Weight of the object at the north pole $m{g}_p=196N$

Acceleration due to gravity, $g=10m/s^2$

The radius of the Earth, $R_e=6400km$

Step 2. Finding the Weight at the equator $m{g}_e$:

As we know, the weight on the equator is given by,

$m{g}_e=m{g}_p-\frac{m{g}_p{v}^2}{R_e}$ ………… $\left(1\right)$

Where $\frac{m{g}_p{v}^2}{R_e}$ is the centrifugal force on the object due to earth rotation, $m{g}_e$ is the weight on the equator and $m{g}_p$is weight on the pole, $R_e$ is the radius of Earth.

The velocity of Earth's rotation is, $v=\frac{2\pi R}{t}=\frac{2\pi R}{24hr}$

Putting the values in the equation $\left(1\right)$, we get

$m{g}_e=196-196\times \frac{{\left(\frac{2\pi R}{24hr}\right)}^2}{R}$

$m{g}_e=196-196\times {\left(\frac{2\pi }{24\times 60\times 60}\right)}^2\times 6400\times {10}^3$

$m{g}_e=196-0.0034\times 196=195.34N$

Hence, option (C) is the correct option.