Question

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 $g = \frac{GM}{R^2} = 9.8 \text{ ms}^{-2}$ and radius of earth, $R = 6400 \text{ km}$.]

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

Hint:

Weight decreases as you move from the poles to the equator due to the centrifugal force caused by Earth's rotation.

Answer 1

The Correct Option is C

Step 1: Weight at pole $W_p = mg = 49 \text{ N}$. Thus, mass $m = \frac{49}{9.8} = 5 \text{ kg}$.
Step 2: Effective gravity at equator $g' = g - R\omega^2$.
Step 3: $R\omega^2$ for Earth is approx $0.0338 \text{ m/s}^2$.
Step 4: $W_e = m(g - R\omega^2) = 5(9.8 - 0.0338) = 49 - 0.169 = 48.831 \text{ N}$.