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

If the density of a planet is double that of the earth and the radius is $1.5$ times that of the earth,the acceleration due to gravity on the surface of the planet is ........

The weight of an object on the surface of the Earth is $72 \, N$. What will be the weight of the object at a height of $R/2$ from the surface of the Earth? ($R$ = radius of the Earth)

What should be the angular speed of the Earth about its axis so that the acceleration due to gravity at the equator becomes zero?

$A$ simple pendulum is oscillating with frequency $F$ on the surface of the earth. It is taken to a depth $R/3$ below the surface of the earth ($R =$ radius of earth). The frequency of oscillation at depth $R/3$ is

The variation of acceleration due to gravity $(g)$ with distance $(r)$ from the center of the earth is correctly represented by ... (Given $R =$ radius of earth)

Vedclass Test Series

Exam Paper Generator

Online Exam Module