# A box weighs 196 N on a spring balance at the north pole.

Question:

A box weighs $196 \mathrm{~N}$ 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 $g=10 \mathrm{~ms}^{-2}$ at the north pole and the radius of the earth $=6400 \mathrm{~km}$ ):

1. (1) $195.66 \mathrm{~N}$

2. (2) $194.32 \mathrm{~N}$

3. (3) $194.66 \mathrm{~N}$

4. (4) $195.32 \mathrm{~N}$

Correct Option: , 4

Solution:

(4) Weight at pole, $w=m g=196 \mathrm{~N}$

$\Rightarrow m=19.6 \mathrm{~kg}$

Weight at equator, $w^{\prime}=m g^{\prime}=m\left(g-\omega^{2} R\right)$

$=19.6\left[10-\left(\frac{2 \pi}{24 \times 3600}\right)^{2} \times 6400 \times 10^{3}\right] \mathrm{N}$

$\left(\because \omega=\frac{2 \pi}{T}\right)$

$=19.6[10-0.034]=195.33 \mathrm{~N}$