Q125 / 150 · MHT CET 2023 (11 May Shift 1) · Physics

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

  • A
    $\frac{1}{80}$
  • B
    $\frac{1}{400}$
  • Correct answer
    C
    $\frac{1}{800}$
  • D
    $\frac{1}{1600}$

Solution

At equator, for the weight to be zero, the gravitational force must be equal to centrifugal force. $$ \begin{aligned} & \mathrm{mR} \omega^2=\mathrm{mg} \\ & \omega^2=\frac{\mathrm{g}}{\mathrm{R}} \\ & \omega=\sqrt{\frac{\mathrm{g}}{\mathrm{R}}} \\ & \omega=\sqrt{\frac{10}{6.4 \times 10^6}} \\ & \omega=\frac{1}{800} \frac{\mathrm{rad}}{\mathrm{s}} \end{aligned} $$

Hence, the correct answer is option: 'C'.

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