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JEE Main 2021 (18 Mar, Shift 2) · Acceleration Due to Gravity

Acceleration Due to Gravity question from JEE Main 2021 (18 Mar, Shift 2)

Q98JEE Main 2021 · 18 MAR · SHIFT 2Medium

Acceleration Due to Gravity

If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately: [Take g = 10 ms−2{}^{-2}, the radius of earth, R = 6400 ×\times 103 m, Take π\pi = 3.14]

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Answer: (a)

  1. Bodies float when ω2R=g⇒ω=gR=106.4×106=1800\omega^2 R = g \Rightarrow \omega = \sqrt{\frac{g}{R}} = \sqrt{\frac{10}{6.4 \times 10^6}} = \frac{1}{800} rad/s
  2. Length of day T=2πω=2×3.14×800=5024T = \frac{2\pi}{\omega} = 2 \times 3.14 \times 800 = 5024 s
  3. T≈83.7T \approx 83.7 min ≈84\approx 84 min
  4. So the answer is (a) 84 minutes.
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