JEE Main 2017 · 8 Apr · Shift 1 · Physics Q7

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PhysicsSingle correct+4 / -1Question 7 of 90

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 weigh $\dfrac34$ W. Radius of the Earth is 6400 km and $g=10$ m/s $^2$ .

1.1\times10^{-3}

rad/s

0.83\times10^{-3}

rad/s

0.63\times10^{-3}

rad/s

0.28\times10^{-3}

rad/s

Answer and worked solution

Official answer: C

At the equator $mg-m\omega^2R=\frac34mg$ , so
$\omega=\sqrt{\frac g{4R}}=\sqrt{\frac{10}{4\times6.4\times10^6}}=6.25\times10^{-4}\approx0.63\times10^{-3}\text{ rad/s}.$

Topics:Variation of g

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JEE Main 2017 · 8 Apr · Shift 1, Physics question 7