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7. gravitation — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics7. gravitation1 Mark
MCQ
What should be the angular speed with which the earth have to rotate on its axis so that a person on the equator would weigh $\frac{3}{5}$ th as much as present?
  • ✓
    $\sqrt{\frac{2 g}{5 R}}$
  • B
    $\sqrt{\frac{2 R}{5 g}}$
  • C
    $\frac{2 \sqrt{R}}{\sqrt{5 g}}$
  • D
    $\frac{2 g}{5 R}$
✓

Answer

Correct option: A.
$\sqrt{\frac{2 g}{5 R}}$
a
(a)

$w=w-m \omega^2 R$

$\Rightarrow m g_e=m g-m \omega^2 R$

$m g_e=\frac{3}{5} m g$

$\Rightarrow m \omega^2 R=\frac{2}{5} m g$

$\Rightarrow \omega=\sqrt{\frac{2 g}{5 R}}$

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