Verified Solution • 2025–26 Session moderate

QJEEM17Ph8753: JEE Main 2017 Physics - Class 11 JEEM17Ph8753 Solution: If the Earth has no rotational motion, the weight of a person…

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

Multiple Choice Options

  • A 1.1 ×\times 10−3 rad/s
  • B 0.83 ×\times 10−3 rad/s
  • C 0.63 ×\times 10−3 rad/s
  • D 0.28 ×\times 10−3 rad/s

Step-by-Step Verified Solution

Initially when earth is not rotating then weight of the person is ww .

When earth rotares about it's axis then weight = 3ω4{{3\omega } \over 4}

Then,

g' = g −- ω\omega 2R cos2 θ\theta

⇒\Rightarrow    \,\,\, 3g4{{3g} \over 4} = g −- ω\omega 2R cos2 0o

⇒\Rightarrow    \,\,\, ω\omega 2R = g4{g \over 4}

   \,\,\, ω\omega = g4R\sqrt {{g \over {4R}}}

⇒\Rightarrow ω=104×6400×103\omega = \sqrt {{{10} \over {4 \times 6400 \times {{10}^3}}}}

= 0.63 ×\times 10 −- 3 rad/s

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