Question

An aeroplane revolves in a circle above the surface of the earth at a fixed height with speed $100km/h$. The magnitude of change in velocity after completing 1/2 revolution will be:

• A. $200km/hr$
• B. $150km/hr$
• C. $300km/hr$
• D. $400km/hr$

Answer 1

The correct option is A $200km/hr$

Change in velocity,

$|v_2-v_1|=\sqrt{v^2+v^2+2v\times v\times \cos \theta }$

$|v_2-v_1|=\sqrt{2v^2+2v^2\cos \theta }$

$|v_2-v_1|=\sqrt{2v^2(1+\cos \theta )}$

$|v_2-v_1|=\sqrt{2v^2\times 2{\sin }^2\frac{\theta }{2}}$

$|v_2-v_1|=2v\sin \frac{\theta }{2}$

$|v_2-v_1|=2\times 100\times \sin \frac{180}{2}$

$|v_2-v_1|=2\times 100\times 1$

$|v_2-v_1|=200km/hr$