First slide

Acceleration due to gravity and its variation

Question

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

Moderate

A

6.2 h
B

1.4 h
C

28 h
D

5.6 h

Solution

$\begin{array}{l} mg = {mRω}^{2} \\ R = radius of earth \\ ω = \sqrt{\frac{g}{R}} \\ T = 2 π \sqrt{\frac{R}{g}} = 2 π \sqrt{640000} \\ = 2 π \times 800 s = \frac{2 π \times 800}{3600} h = 1 .39 h = 1 .4 h \end{array}$

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