Question

How many hours would make a day if earth were rotating at such a high speed that the weight of a body on the equator were zero

• A. $6.2h$
• B. $1.4h$
• C. $28h$
• D. $5.6$

Answer 1

Answer: (B)

$1.4h$

Let $\omega$ be the angular velocity of rotating earth.

For the weight of the body on equator to be zero, $mg=m{\omega }^{2}R$

$⟹\omega =\sqrt{\frac{g}{R}}$

Thus the time period of one rotation=$\frac{2\pi }{\omega }=2\pi \sqrt{\frac{R}{g}}$

$R=6400km,g=9.8m/s^2$

$⟹T\approx 1.4h$