If the Earth is assumed to be a sphere of rad | vedclass

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

Question

(B) The acceleration due to gravity at a latitude $\lambda$ is given by the formula:$g' = g - R{\omega ^2}{\cos ^2}\lambda$where $g$ is the accelerati

Vedclass · Accepted Answer

$\frac{3}{4}{\omega ^2}R$

Vedclass · Answer

(B) The acceleration due to gravity at a latitude $\lambda$ is given by the formula:$g' = g - R{\omega ^2}{\cos ^2}\lambda$where $g$ is the acceleration due to gravity at the equator (ignoring the centrifugal effect) or the effective gravity at the equator where $\lambda = 0^\circ$.At latitude $\lambda = 30^\circ$:$g_{30} = g - R{\omega ^2}{\cos ^2}30^\circ$Since $\cos 30^\circ = \frac{\sqrt{3}}{2}$,we have $\cos^2 30^\circ = \frac{3}{4}$.Substituting this into the equation:$g_{30} = g - R{\omega ^2} \left( \frac{3}{4} \right)$Therefore,the difference is:$g - g_{30} = \frac{3}{4}{\omega ^2}R$.

If the Earth is assumed to be a sphere of radius $R$,and $g_{30}$ is the value of acceleration due to gravity at a latitude of $30^\circ$ and $g$ is the value at the equator,the value of $g - g_{30}$ is:

Similar Questions

If the change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $x$ below it,then (both $x$ and $h$ being much smaller than the radius of the earth)

Assuming the Earth to be a sphere of uniform mass density,how much would a body weigh (in $N$) halfway down to the centre of the Earth if it weighed $250 \; N$ on the surface?

Assuming the density of the Earth is constant, which graph correctly represents the variation of acceleration due to gravity $(g)$ with the distance $(r)$ from the center of the Earth (radius of the Earth $= R$)?

How much is the radius of the Earth at the equator greater than the radius at the poles?

Derive the equation for the variation of acceleration due to gravity $g$ with depth $d$ below the surface of the Earth.

Vedclass Test Series

Exam Paper Generator

Online Exam Module