Question

If the earth has no rotational motion, the weight of a person on the equation is W. Detrmine the speed with which the earth would have to rotate about its axis so that the person at the equator will weight 34 W. Radius of the earth is 6400 km and g = 10 m/s².

A. 0.63×10⁻³ rad/s
B. 0.28×10⁻³ rad/s
C. 1.1×10⁻³ rad/s
D. 0.83×10⁻³ rad/s

Answer 1

To determine the speed with which the Earth would have to rotate about its axis so that a person at the equator weighs 34 times their original weight, the formula for centripetal force and gravitational force is used. The correct answer is D. 0.83×10⁻³ rad/s.

Step-by-step explanation:

To determine the speed with which the Earth would have to rotate about its axis so that a person at the equator weighs 34 times their original weight, we can use the relationship between centripetal force and gravitational force.

The centripetal force is given by the formula: F = mv²/r, where F is the centripetal force, m is the mass of the person, v is the speed of rotation, and r is the radius of the Earth.

The gravitational force is given by the formula: F = mg, where m is the mass of the person and g is the acceleration due to gravity.

Equating these two forces gives mv²/r = mg. Since we want the person to weigh 34 times their original weight, we can substitute 34mg for mv²/r and solve for v:

v = √(34gR)

Substituting the known values g = 10 m/s² and R = 6400 km = 6.4 × 10⁶ m into the formula gives v = 0.83 × 10⁻³ rad/s. Therefore, the correct option is D. 0.83×10⁻³ rad/s.