First slide

Variation of g

Question

The speed of earth's rotation about its axis is $ω$ Its speed is increases to x times to make the effective acceleration due to gravity equal to zero at the equator. Then x is

Moderate

A

1
B

8.5
C

17
D

34

Solution

$\begin{array}{l} ω = \frac{2 π}{24 \times 3600} \\ g^{'} = g - R_{e} ω^{2} or 0 = g - R_{e} ω^{2} \end{array}$
or , $ω^{'} = \sqrt{(\frac{g}{R_{e}})}$
$\begin{array}{l} ω^{'} = \frac{2 π}{84 \cdot 6 \times 60} \\ ∴ \frac{ω^{'}}{ω} = \frac{24 \times 3600}{84 \cdot 6 \times 60} = 17 \end{array}$

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