What should be the angular speed of the Earth | vedclass

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

Question

(A) The effective acceleration due to gravity $g'$ at a latitude $\lambda$ is given by $g' = g - \omega^2 R \cos^2 \lambda$. For the body to be weight

Vedclass · Accepted Answer

$2.5 	imes 10^{-3} \, rad/sec$

Vedclass · Answer

(A) The effective acceleration due to gravity $g'$ at a latitude $\lambda$ is given by $g' = g - \omega^2 R \cos^2 \lambda$. For the body to be weightless,the effective gravity must be zero,so $g' = 0$. Substituting the values: $0 = g - \omega^2 R \cos^2(60^{\circ})$. Since $\cos(60^{\circ}) = 1/2$,we have $\cos^2(60^{\circ}) = 1/4$. Thus,$g = \omega^2 R (1/4) \implies \omega^2 = 4g/R$. Taking the square root,$\omega = 2 \sqrt{g/R}$. Using $g = 9.8 \, m/s^2$ and $R = 6.4 	imes 10^6 \, m$: $\omega = 2 \sqrt{9.8 / (6.4 	imes 10^6)} \approx 2 \sqrt{1.53 	imes 10^{-6}} \approx 2 	imes 1.237 	imes 10^{-3} \approx 2.47 	imes 10^{-3} \, rad/s$. Rounding to the nearest option,$\omega = 2.5 	imes 10^{-3} \, rad/s$.

What should be the angular speed of the Earth so that a body at $60^{\circ}$ latitude becomes weightless? (Radius of Earth $R = 6400 \, km$)

Similar Questions

An astronaut inside a small spaceship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size,can he hope to detect gravity?

The time period of a simple pendulum increases by a factor of $\sqrt{2}$ at a height $h$ from the surface of the Earth. Then the value of $h$ is:

$A$ body weighs $W$ newton on the surface of the earth. Its weight at a height equal to half the radius of the earth will be:

The angular speed of the Earth in $rad/s$,so that bodies on the equator may appear weightless is: [Use $g = 10\, m/s^2$ and the radius of the Earth $R = 6.4 \times 10^3\, km$]

The radii of two planets $A$ and $B$ are $R$ and $4R$ and their densities are $\rho$ and $\rho/3$ respectively. The ratio of acceleration due to gravity at their surfaces $(g_A : g_B)$ will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module