Question

The time period of rotation of the earth around its axis so that the objects at the equator become weightless is nearly ($g=9.8m/s^2$ , Radius of earth $=$ 6400km.)

• A. $64min$
• B. $74min$
• C. $84min$
• D. $94min$

Answer 1

Answer: (C)

$84min$

For the weight to be zero at the equator, value of gravity should be zero. i.e
$g{}^{\prime }=g-R(\omega {}^{\prime }{)}^2=0$
$\Rightarrow {\omega }^{{}^{\prime }}=\sqrt{\frac{g}{R}}=123.7\times {10}^{-5}{s}^{-1}$
So, time period($T$) is calculated using:
$T=\frac{2\pi }{{\omega }^{\prime }}=\frac{2\pi }{123.7}\times {10}^{5}s=5079.4s=84.66min$