Question

Suppose that Earth rotated much faster on its axis-so fast that people were almost weightless when at Earth's surface. How long would the length of a day be on this new Earth? Assume that rE = 6.37×106 m is the radius of Earth.

Answer 1

Answer:

1.4 hour

Explanation:

radius of earth, r = 6.37 x 10^6 m

The acceleration due to gravity due to the effect of rotation of earth is given by

$g' = g\left ( 1-\frac{r\omega ^{2}}{g} \right )$

As the object is weightless, so, g' = 0

$\omega=\sqrt\frac{g}{r}$

$T=2\pi \sqrt\frac{r}{g}$

$T=2\pi \sqrt\frac{6.37\times 10^{6}}{9.8}$

T = 5063.09 seconds

T = 1.4 hour