Question

The speed with which the earth would have to rotate about its axis so that a person on the equator would weight `3/5`th as much at present is ______.

(g = gravitational acceleration, R = equatorial radius of the earth)

Options

• `sqrt((2g)/(5R))`

• `sqrt((3g)/(5R))`

• `sqrt((5R)/(2g))`

• `sqrt(3/5)gR`

Answer 1

The speed with which the earth would have to rotate about its axis so that a person on the equator would weight `3/5`th as much at present is `underlinebb(sqrt((2g)/(5R)))`.

Explanation:

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

`g^' = g - Romega^2cosPhi`

At the equator, Φ = 0

⇒ `g^' = g - Romega^2`

Weight of person at the equator, `mg^' = mg - mRomega^2`

⇒ `3/5mg = mg - mRomega^2`

⇒ `omega^2 = (2g)/(5R)` or `omega = sqrt((2g)/(5R))`