Question

An aeroplane is moving on a circular path with a speed $250 km/h$. What is the change in velocity in half revolution?
A. $0$
B. $125km/h$
C. $250 km/h$
D. $500km/h$

Answer 1

Hint: In a uniform circular motion, the magnitude of the velocity is constant, but the direction, which is the tangent at any point, varies at every point. And the change in velocity is given by$change\; in \; velocity\;=final\; velocity\;-\;initial\;velocity$
Formula used: $change\; in \; velocity\;=final\; velocity\;-\;initial\;velocity$

Complete step-by-step answer:
In circular motion, the object moves in the perimeter of the circle. If the motion is uniform, then the object moves at a constant speed. But, since velocity is a vector quantity, it has a constant magnitude and a varying direction. The direction of velocity in a circular path is given by the tangent at the point, which points at a new direction at every point.
Here since the aeroplane is moving in a circular path, the direction of velocity gets reversed after half revolution. Say, AB is the diameter of the circular path, and if the aeroplane starts at A, after a revolution it will reach A again. Then for half revolution it will reach B. i.e. if velocity is $+250km/hr$ at a point A, then at point B its velocity is $-250km/hr$
Then the change in velocity will be given by,
$change\; in \; velocity\;=final\; velocity\;-\;initial\;velocity=-250-(+250)=-500km/hr$
Hence the answer is D. $500km/h$

Note: Even in uniform circular motion, after half revolution the direction of velocity of the object gets reversed. For simplicity, we can consider the diameter of the circle, to understand half revolution, where the points which join the diameter, are the points where the velocity gets exactly reversed.