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JEE Main 2017 (8 Apr, Shift 1) · Acceleration Due to Gravity

Acceleration Due to Gravity question from JEE Main 2017 (8 Apr, Shift 1)

Q118JEE Main 2017 · 8 APR · SHIFT 1Medium

Acceleration Due to Gravity

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 34\frac{3}{4} W. Radius of the Earth is 6400 km and g=10 m/s2.

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Answer: (c)

  1. At the equator: m(g−ω2R)=34mg⇒ω2=g4Rm(g - \omega^2 R) = \frac{3}{4}mg \Rightarrow \omega^2 = \frac{g}{4R}
  2. ω=104×6.4×106=3.9×10−7\omega = \sqrt{\frac{10}{4 \times 6.4 \times 10^6}} = \sqrt{3.9 \times 10^{-7}}
  3. ω≈6.25×10−4≈0.63×10−3\omega \approx 6.25 \times 10^{-4} \approx 0.63 \times 10^{-3} rad/s
  4. So the answer is (c).
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