Question

A body weighs $49N$ 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 $g=GM/R^2=9.8m{s}^{-2}$ and radius of earth,$R=6400km$]

• A. $49N$
• B. $49.83N$
• C. $49.17N$
• D. $48.83N$

Answer 1

The correct option is D

$48.83N$

Step 1. Given data: Weight, $W$ at north pole $=49N$

Step 2. The formula used: Apparent acceleration due to gravity at the equator, $g^{\text{'}}=g-{\omega }^{2}R$where,$\omega$ is the angular velocity, $R$is the radius of the earth, $g$is the acceleration due to gravity.

Step 3: Calculate the apparent weight at the equator,

$M{g}^{\text{'}}=M(g-{\omega }^{2}R)....\left(i\right)$

From $\left(i\right)$, the weight at the equator will be less than the weight at the North pole.

The only correct value out of all the options is $48.83N$.

Hence the weight of the body at the equator is $48.83N$.

The correct option is D.