First slide

Acceleration due to gravity and its variation

Question

In order to make the effective acceleration due to gravity equal to zero at the equator, the angular velocity of rotation of the earth about its axis should be $(g = 10 {ms}^{- 2}$ and radius of earth is 6400 kms)

Moderate

A

$0 rad \sec^{- 1}$
B

$\frac{1}{800} rad \sec^{- 1}$
C

$\frac{1}{80} rad \sec^{- 1}$
D

$\frac{1}{8} rad \sec^{- 1}$

Solution

$g^{'} = g - ω^{2} {Rcos}^{2} λ$
For weightlessness at equator $λ = 0$ and $g' = 0$
$∴ 0 = g - ω^{2} R \Rightarrow ω = \sqrt{\frac{g}{R}} = \frac{1}{800} \frac{rad}{s}$

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