Question 189: Gravitation

Question

The acceleration due to gravity on the earth’s
surface at the poles is g and angular velocity of
the earth about the axis passing through the
pole is $$\omega $$. An object is weighed at the equator
and at a height h above the poles by using a
spring balance. If the weights are found to be
same, then h is (h << R, where R is the radius
of the earth)

Accepted Answer

At equator, g
1
= g - R$${\omega ^2}$$
At height h, g
2
= $$g\left( {1 - {{2h} \over R}} ight)$$ [as given h << R]
$$ \because $$ Weight same at poles and at h (so g
1
= g
2
)
$$ 	herefore $$ g - R$${\omega ^2}$$ = $$g\left( {1 - {{2h} \over R}} ight)$$
$$ \Rightarrow $$ $${R{\omega ^2} = {{2gh} \over R}}$$
$$ \Rightarrow $$ $${h = {{{R^2}{\omega ^2}} \over {2g}}}$$

Answer

$${{{R^2}{\omega ^2}} \over {2g}}$$

Answer

$${{{R^2}{\omega ^2}} \over g}$$

Answer

$${{{R^2}{\omega ^2}} \over {8g}}$$

Answer

$${{{R^2}{\omega ^2}} \over {4g}}$$

Gravitation

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