Question

An artificial satellite is moving in a circular orbit of radius $42250km.$ Calculate its speed if it takes 24 hours to revolve around the earth.

Answer 1

Hint: This is a very straight forward question. Radius of circle has given. Path travel by satellite is circular. To find out the distance covered by an artificial satellite, use the formula of circumference of the circle. Then use the formula of speed. Convert the hour into seconds by multiplying 3600 to 24. Unit of speed is km/s or m/s.

Complete step by step solution:
In this question it is given that a satellite is moving in a circular orbit of radius $42250 km$. The satellite completes only one revolution which is circular path in 24hour. Now we need to find velocity to travel $42250km$ in 24 hour by artificial satellite.
We know that satellites cover the circumference of a circular path in 24 hour.
So, $\begin{aligned} & c=2\pi r \\\ & c=2\times 3.14\times 42250=265464.58km \\\ \end{aligned}$
Now to find the speed of the satellite, we know that speed is nothing but distance covered by body per unit time.
So, $\text{speed=}\dfrac{\text{distance travelled}}{\text{time taken}}$
$s=\dfrac{265464.58}{24\times 60\times 60}=3.07km/s$
So the speed of an artificial satellite in 24 hours is 3.07km/s.

Note: Students usually make mistakes in considering the value of distance. They directly put the value of distance in the speed formula. Don’t do that. Understand that path is circular, not straight. If the path is circular, then you must have considered circumference of circular and if the path is straight (that is from the centre of a circle to point on circumference) then you can directly value distance value in speed. Some students may get confused in the speed and velocity formula. Speed is nothing but distance per unit time while velocity is nothing but displacement per unit time.