Question

A body on the surface of the earth at latitude ${60}^o$ will be under weight lessness state if the angular velocity of rotation of the earth becomes

• A. $\sqrt{\frac{GM}{R^3}}$
• B. $\sqrt{\frac{2GM}{R^3}}$
• C. $\sqrt{\frac{GM}{{2R}^3}}$
• D. $\sqrt{\frac{4GM}{R^3}}$

Answer 1

The correct option is B $\sqrt{\frac{2GM}{R^3}}$

For weightlessness condition the effective value of g i.e.,

$g_{eff}=0$ (As $m{g}_{eff}=$ weight $=0$)

At a given latitude$\left(\theta \right)$ the expression of $g_{eff}$ is:

$g_{eff}=g-R{\omega }^2\cos \theta$ (R$=$ radius of Earth)

Here latitude$={60}^o$

$\Rightarrow g-R{\omega }^2\cos {60}^o=0$

$\Rightarrow \omega =\sqrt{\frac{2g}{R}}$

Also $g=\frac{GM}{R^2}$(Where M$=$mass of Earth)

$\Rightarrow \omega =\sqrt{\frac{2GM}{R^3}}$ is new the angular velocity of Earth.