Question

A box weighs $196\text{N}$ 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 $g=10{\text{ms}}^{-2}$ at the North Pole and the radius of the earth $=6400\text{km})$

• A. $195.66\text{N}$
• B. $194.32\text{N}$
• C. $194.66\text{N}$
• D. $195.32\text{N}$

Answer 1

The correct option is D $195.32\text{N}$

$\text{Weight at pole},W_p=mg=196\text{N}$
$\Rightarrow m=19.6\text{kg}$
Considering the effect of rotation of earth in acceleration due to gravity,

$\text{Weight at the equator,}{W}^{\prime }=m{g}^{\prime }$

$W^{\prime }=m(g-{\omega }^{2}R)$
$\because \omega =\frac{2\pi }{T},T=24\text{hours}$
$W^{\prime }=19.6[10-{\left(\frac{2\pi }{24\times 3600}\right)}^2\times 6400\times {10}^3]$
$W^{\prime }=19.6[10-0.034]=195.33\text{N}$

Hence, option $\left(D\right)$ is correct.