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 (3W)/4. Radius of the Earth is 6400 km and g=10 m/s².

Question

Accepted Answer

(1) 0.63×10⁻³ rad/s. At the equator the apparent weight is m(g-ω²R), and this must equal 3/4mg. So the lost part is ω²R=g/4. ω=√g/(4R)=√(10)/(4×6.4×10⁶)=√3.906×10⁻⁷. That gives ω=6.25×10⁻⁴≈0.63×10⁻³ rad/s.

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 (3W)/4. Radius of the Earth is 6400 km and g=10 m/s².

Step-by-step solution

Why the other options are wrong