If the Earth has no rotational motion,the wei | vedclass

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

Question

(C) The effective acceleration due to gravity at the equator (where $	heta = 0^\circ$) is given by $g' = g - \omega^2 R$.Given that the weight become

Vedclass · Accepted Answer

$0.63 	imes 10^{-3} \ rad/s$

Vedclass · Answer

(C) The effective acceleration due to gravity at the equator (where $	heta = 0^\circ$) is given by $g' = g - \omega^2 R$.Given that the weight becomes $\frac{3}{4} W$,the effective gravity must be $g' = \frac{3}{4} g$.Substituting this into the equation: $\frac{3}{4} g = g - \omega^2 R$.Rearranging for $\omega^2 R$: $\omega^2 R = g - \frac{3}{4} g = \frac{1}{4} g$.Solving for $\omega$: $\omega = \sqrt{\frac{g}{4R}}$.Given $g = 10 \ m/s^2$ and $R = 6400 \ km = 6.4 	imes 10^6 \ m$.$\omega = \sqrt{\frac{10}{4 	imes 6.4 	imes 10^6}} = \sqrt{\frac{10}{25.6 	imes 10^6}} = \sqrt{\frac{1}{2.56 	imes 10^6}} = \frac{1}{1.6 	imes 10^3} \ rad/s$.$\omega = 0.625 	imes 10^{-3} \ rad/s \approx 0.63 	imes 10^{-3} \ rad/s$.

If the Earth has no rotational motion,the weight of a person on the equator is $W$. Determine the speed with which the Earth would have to rotate about its axis so that the person at the equator will weigh $\frac{3}{4} W$. The radius of the Earth is $6400 \ km$ and $g = 10 \ m/s^2$.

Similar Questions

The mass of the moon is $(1/8)$ of the earth,but the gravitational pull is $(1/6)$ of the earth. This is due to the fact that:

$A$ body weighs $300 \ N$ on the surface of the earth. How much will it weigh at a distance $\frac{R}{2}$ below the surface of the earth (in $N$)? ($R$ is the radius of the earth.)

Which of the following statements are true about the acceleration due to gravity,$g$?
$A$. $g$ is greater at the poles.
$B$. The value of $g$ decreases with height.
$C$. The value of $g$ is the same all over the Earth.
$D$. The value of $g$ is maximum at the center of the Earth.

$A$ hole is drilled halfway to the center of the Earth. $A$ body weighs $300 \ N$ on the surface of the Earth. How much will it weigh at the bottom of the hole (in $N$)?

Weight of a body of mass $m$ decreases by $1\%$ when it is raised to height $h$ above the Earth's surface. If the body is taken to a depth $h$ in a mine,then its weight will

Vedclass Test Series

Exam Paper Generator

Online Exam Module