The radius of earth is 6400 km and acceleration due to gravity g = 10 m s⁻². For the weight of body of mass 5 kg to be zero on equator, rotational velocity of the earth must be (in rad/s) (a) 1/80 (b) 1/400 (c) 1/800 (d) 1/1600

Answer: (c). Weightless at equator: g - ω² R = 0 ⇒ ω = √(g/R) (mass does not matter) ω = √((10)/(6.4 × 10⁶)) = 1/800 rad/s So the answer is (c) 1/800.

The radius of earth is 6400 km and acceleration due to gravity g = 10… | MHT CET 2023 (11 May, Shift 1)

Q71MHT CET 2023 · 11 MAY · SHIFT 1Medium

Acceleration Due to Gravity

The radius of earth is $6400\text{ km}$ and acceleration due to gravity $g = 10\text{ m s}^{-2}$ . For the weight of body of mass $5\text{ kg}$ to be zero on equator, rotational velocity of the earth must be (in $\text{rad/s}$ )

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Answer: (c)

Weightless at equator: $g - \omega^2 R = 0 \Rightarrow \omega = \sqrt{\frac{g}{R}}$ (mass does not matter)
$\omega = \sqrt{\frac{10}{6.4 \times 10^6}} = \frac{1}{800}$ rad/s
So the answer is (c) $\frac{1}{800}$ .

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Acceleration Due to Gravity question from MHT CET 2023 (11 May, Shift 1)

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