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Find the angular velocity of a satellite which revolves in a circular orbit of radius $35000 km$ and completes one round in $12$ hours?

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\frac{π}{3} rad / hr

\frac{π}{6} rad / hr

\frac{π}{4} rad / hr

\frac{π}{2} rad / hr

answer is B.

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Detailed Solution

The angular velocity of a satellite which revolves in a circular orbit of radius

35000 km

and completes one round in

12

hours is

\frac{π}{6} rad / hr

.
Given
Radius of the circular orbit

= 35000 km

.
Time taken to complete one round

= 12 hrs

.
Angle subtended at the centre

= 36 0^{o}

[ ∵ Earth is approximately circular].
∵

36 0^{o} = 2 π rad

.
∴ Angle subtended at the centre

= 2 π

Now using the formula,
Angular Velocity

ω =

Angle subtended at the centre in radians/Time taken to complete

1

round.
∴

ω = \frac{2 π}{12}

= \frac{π}{6}

∴ Angular velocity of the satellite is

\frac{π}{6} rad / hr

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