JEE Mains · Physics · STD 11 - 7. gravitation
If the Earth has no rotational motion, the weight of a person on the equator is \(W\). Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weight \(\frac{3}{4}\,W\) . Radius of the Earth is \(6400\, km\) and \(g = 10\, m/s^2\)
- A \(1.1 \times {10^{ - 3}}\,rad/s\)
- B \(0.83 \times {10^{ - 3}}\,rad/s\)
- C \(0.63 \times {10^{ - 3}}\,rad/s\)
- D \(0.28 \times {10^{ - 3}}\,rad/s\)
Answer & Solution
Correct Answer
(C) \(0.63 \times {10^{ - 3}}\,rad/s\)
Step-by-step Solution
Detailed explanation
We know, \(g' = g - {\omega ^2}R{\cos ^2}\theta \) \(\frac{{3g}}{4} = g - {\omega ^2}R\) \(Given,\,g' = \frac{3}{4}g\) \({\omega ^2}R = \frac{g}{4}\) \(\omega = \sqrt {\frac{g}{{4R}}} = \sqrt {\frac{{10}}{{4 \times 6400 \times {{10}^{ - 3}}}}} \)…
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