Question

The time period of rotation of the earth around its axis so that the objects at the equator become weightless is nearly (g = 9.8$m/s^2$, radius of earth = 6400 km.)
(A) 64 min
(B) 74 min
(C) 84 min
(D) 94 min

Answer 1

Hint: To answer this question we should be knowing the equation to determine the gravity at the equator of the earth. Once we obtain the formula we have to put the values mentioned in the question to obtain the angular velocity. From the value of angular velocity, we have to obtain the value of time period. This will give us the required answer.

Complete step by step solution:
We should know that for the weight to be zero at the equator, the value of the gravity should be zero. So we can write that:
Here ${\omega }^{/}$ represents the angular velocity of the earth.
We can write the equation as:
$\Rightarrow {\omega }^{/}=\sqrt{{\displaystyle \frac{g}{R}}}$
Put the values now in the about formula:
$\Rightarrow {\omega }^{/}=123.7\times {10}^{-5}{s}^{-1}$
So now the time period or T is calculated using the below stated formula:
$T={\displaystyle \frac{2\pi }{{\omega }^{/}}}={\displaystyle \frac{2\pi }{123.7}}\times {10}^{5}s$
Evaluating the above equation, we get that:
T = 5079.4s = 84.66 min
So we can say that the time period of rotation of the earth around its axis so that the objects at the equator become weightless is nearly 84 min.

Hence the correct answer is option C.

Note: In the answer we have come across the term angular velocity. For better understanding we should know the meaning of the term. By angular velocity we mean the rate at which the earth rotates around the axis. This is usually expressed in radians or even revolutions per second or minute.