If all objects on the equator of the earth fe | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) For an object on the equator to feel weightless,the effective acceleration due to gravity must be zero.The effective acceleration due to gravity a

Vedclass · Accepted Answer

$1.41$

Vedclass · Answer

(D) For an object on the equator to feel weightless,the effective acceleration due to gravity must be zero.The effective acceleration due to gravity at the equator is given by $g_{eff} = g - \omega^2 R$,where $g$ is the acceleration due to gravity,$\omega$ is the angular velocity of the earth,and $R$ is the radius of the earth.Setting $g_{eff} = 0$,we get $g - \omega^2 R = 0$,which implies $\omega^2 R = g$.Thus,$\omega = \sqrt{\frac{g}{R}}$.The duration of the day (time period $T$) is given by $T = \frac{2 \pi}{\omega} = 2 \pi \sqrt{\frac{R}{g}}$.Substituting the values $R \approx 6.4 	imes 10^6 \, m$ and $g \approx 9.8 \, m/s^2$:$T = 2 	imes 3.14 	imes \sqrt{\frac{6.4 	imes 10^6}{9.8}} \approx 2 	imes 3.14 	imes 808 \, s \approx 5074 \, s$.Converting to hours: $T \approx \frac{5074}{3600} \, hr \approx 1.41 \, hr$.

If all objects on the equator of the earth feel weightless,then the duration of the day will nearly become ....... $hr$.

Similar Questions

What should be the angular velocity of the Earth due to rotation about its own axis so that the weight of an object at the equator becomes $3/5$ of its initial value? (Radius of Earth at the equator is $R = 6400 \, km$,take $g = 10 \, m/s^2$)

The acceleration due to gravity on the surface of the Earth is $g$. What is the acceleration due to gravity at a height $h = R$ above the Earth's surface,where $R$ is the radius of the Earth?

If the Earth loses its gravity,then for a body:

$A$ uniform solid sphere of radius $R$ produces a gravitational acceleration of $a_o$ on its surface. The distance of the point from the centre of the sphere where the gravitational acceleration becomes $\frac{a_o}{4}$ is,

Suppose that the force of earth's gravity suddenly disappears,choose the correct answer out of the following statements.

Vedclass Test Series

Exam Paper Generator

Online Exam Module