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

If it is assumed that the spinning motion of the Earth increases,then the weight of a body on the equator

Identify the incorrect statement. The acceleration due to gravity $g$ decreases if:

At what height above the earth's surface does the acceleration due to gravity fall to $1\%$ of its value at the earth's surface (in $,R$)?

$A$ body weighs $49 \, N$ on a spring balance at the North Pole. What will be its weight recorded on the same weighing machine if it is shifted to the equator (in $, N$)? (Use $g = \frac{GM}{R^2} = 9.8 \, m/s^2$ and radius of the Earth,$R = 6400 \, km$.)

For a sphere of mass $M$ and radius $R$,if the gravitational forces at distances $r_1$ and $r_2$ from the center are $F_1$ and $F_2$ respectively,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module