Question

If the Earth has no rational 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 $m/s^2$ .

• A. $1.1\times {10}^{-3}rad/s$
• B. $0.63\times {10}^{-3}rad/s$
• C. $0.28\times {10}^{-3}rad/s$
• D. $0.83\times {10}^{-3}rad/s$

Answer 1

Answer: (B)

$0.63\times {10}^{-3}rad/s$

$w=mg$

$mg=m{w}^{2}R=\frac{3w}{4}$

$w=m{w}^{2}Rr=\frac{3w}{4}$

$m{w}^{2}R=\frac{w}{4}$

$m{w}^{2}R=\frac{w}{4}$

$w=\sqrt{\frac{w}{4mR}}=\sqrt{\frac{wg}{4wR}}=\sqrt{\frac{g}{4R}}$

$=\sqrt{\frac{10}{4\times 6900\times {10}^3}}$=$\sqrt{\frac{1}{2^2\times 8^2\times {100}^2}}=0.625\times {10}^{-3}rad/s$