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 $\frac{3}{4} W$ . Radius of the Earth is $6400 km$ and $g = 10 m / s^{2}$ .

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$0.83 \times 10^{- 3} r a d / s$

$0.63 \times 10^{- 3} r a d / s$

$0.28 \times 10^{- 3} r a d / s$

$1.1 \times 10^{- 3} r a d / s$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Here, the weight of person on the equator $= W$ .

If Earth rotates about its axis, then weight $= \frac{3 W}{4}$

Radius of the Earth $= 6400 km$

The acceleration due to gravity at the equator, $g_{e} = g - ω^{2} R \cos^{2} θ$

$\frac{3}{4} g = g - ω^{2} R \cos^{2} 0 ° or ω^{2} R = \frac{g}{4} ω = \sqrt{\frac{g}{4 R}} = \sqrt{\frac{10}{4 \times 6400 \times 10^{3}}} = 0.63 \times 10^{- 3} rad / s$

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!