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7.Gravitation
medium
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
$0.28 \times {10^{ - 3}}\,rad/s$
(JEE MAIN-2017)
Solution
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}}}}} $
$ = \frac{1}{{2 \times 8 \times 1000}} = 0.6 \times {10^{ – 3}}\,rad/s$
Standard 11
Physics
