Question

An aeroplane is flying with a uniform speed of 100km/h along the circumference of a circle. The change in velocity in half the revolution will be?
A. 100
B. 150
C. 200
D. 300

Answer 1

Hint:Velocity is a vector quantity while speed is a scalar quantity. Speed gives the magnitude of the velocity, and is not necessary that speed and velocity are equal. In the above case, when the aeroplane moves half the circle, its speed remains the same but the direction of velocity is in the opposite direction.

Complete step by step answer:A particular quantity can be categorized into two types; one is scalar while the other is vector. Scalar quantities have magnitude but they do not have direction, for example distance or temperature. Vector quantities are the quantities that have magnitude as well as direction, such as displacement or acceleration. Velocity is a vector quantity.

It is given that the aeroplane is moving at a uniform speed of 100km/h. Let its velocity be at a directional vector of\[{v_1} = 100\hat i\]. Thus, when it rotates half circle, the direction of velocity, which is always perpendicular, that is tangential to the circle, would be in the opposite direction.

Thus, velocity when the aeroplane rotates half circle would\[{v_2}\]such that\[{v_2} = - 100\hat i\]

Now, the relative velocity of a particle is its final velocity minus the initial=al velocity of the particle. Hence the change in velocity would be as follows:
\[
\Delta v = {v_2} - {v_1} \\
\Delta v = - 100 - 100 \\
\Delta v = - 200\hat i\dfrac{{km}}{h} \\
\]

Thus the change in velocity is 200km/h.

Thus, option (C) is the correct answer.

Notes:Here, we are assuming that the aeroplane is constantly flying along the circumference of the circle and this can only happen when the centripetal force and the gravitational force are cancelling each other out and hence the Newton’s third law of motion is satisfied. Also, here we neglect the force due to air resistance.