Question

What would be the angular speed of earth,so that bodies lying on equator may experience weightlessness?(g=10m/s2 and radius of earth=6400km)

Answer 1

The apparent weight of a person on the equator (Lattitude $ \alpha =0$) is given by

$W'=W-mR_ew^2$

$g'=g -R_e w^2$

$g'=0$

$g-Rw^2=0$

$w=\sqrt {\large\frac{g}{R}}$

$\quad=\sqrt {\large\frac{10}{6400 \times 10^3}}$

$\quad=1.25 \times 10^{-3} rad /s$

Hence a is the correct answer.