Question 221: Gravitation

Question

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

Accepted Answer

Initially when earth is not rotating then weight of the person is $$w$$.
When earth rotares about it's axis then weight = $${{3\omega } \over 4}$$
Then,
g' = g $$-$$ $$\omega $$
2
R cos
2
$$	heta $$
$$ \Rightarrow $$ $$\,\,\,$$ $${{3g} \over 4}$$ = g $$-$$ $$\omega $$
2
R cos
2
0
o
$$ \Rightarrow $$ $$\,\,\,$$ $$\omega $$
2
R = $${g \over 4}$$
$$\,\,\,$$ $$\omega $$ = $$\sqrt {{g \over {4R}}} $$
$$ \Rightarrow $$ $$\omega  = \sqrt {{{10} \over {4 	imes 6400 	imes {{10}^3}}}} $$
= 0.63 $$ 	imes $$ 10
$$-$$3
rad/s

Answer

1.1 $$ 	imes $$ 10−3  rad/s

Answer

0.83 $$ 	imes $$ 10−3  rad/s

Answer

0.63 $$ 	imes $$ 10−3  rad/s

Answer

0.28 $$ 	imes $$ 10−3  rad/s

Gravitation

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

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