If a man at the equator would weigh (3/5)^{th | vedclass

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

Question

(A) At the equator,the effective acceleration due to gravity $g'$ is given by $g' = g - \omega^2 R$,where $g$ is the acceleration due to gravity at th

Vedclass · Accepted Answer

$\sqrt {\frac{2}{5} \frac{g}{R}} $

Vedclass · Answer

(A) At the equator,the effective acceleration due to gravity $g'$ is given by $g' = g - \omega^2 R$,where $g$ is the acceleration due to gravity at the poles,$\omega$ is the angular speed of the Earth,and $R$ is the radius of the Earth.Given that the man's weight at the equator is $(3/5)$ of his actual weight,we have $W' = (3/5)W$.Since $W = mg$,this implies $mg' = (3/5)mg$,which simplifies to $g' = (3/5)g$.Substituting this into the equation for effective gravity: $(3/5)g = g - \omega^2 R$.Rearranging the terms: $\omega^2 R = g - (3/5)g = (2/5)g$.Solving for $\omega$: $\omega^2 = (2/5)(g/R)$,therefore $\omega = \sqrt{(2/5)(g/R)}$.

If a man at the equator would weigh $(3/5)^{th}$ of his weight,the angular speed of the earth is

Similar Questions

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)

The speed with which the earth would have to rotate about its axis so that a person on the equator would weigh $\frac{3}{5}$ th as much as at present weight is ($g=$ gravitational acceleration,$R=$ equatorial radius of the earth).

The speed with which the earth would have to rotate about its axis so that a person on the equator would weigh $\frac{1}{6}$ th as much as at present is ($g=$ gravitational acceleration,$R=$ equatorial radius of the earth).

Two planets have radii $R_1$ and $R_2$ and densities $\rho_1$ and $\rho_2$ respectively. Find the ratio of the acceleration due to gravity on these planets.

At what distance above and below the surface of the earth will a body have the same weight? (Take the radius of the earth as $R$.)

Vedclass Test Series

Exam Paper Generator

Online Exam Module