Question

A particle travels two and a half revolutions of a circle of radius R in time t. The ratio of the average speed of the particle to the magnitude of the average velocity in this time interval is: 1.) π/2 2.) 5π/2 3.) 5π/√2 4.) π/5√2

Answer 1

AnSwer:

★In half revolution of circle with radius (R).

$\implies \sf \: Average \: Speed = \dfrac{\pi \: r}{t} \: - - - (1)$

$\implies \sf \: Average \: Velocity = \dfrac{2r}{t} \: - - - (2)$

Now,

From eqn (1) and (2),

$\bigstar \sf \: Ratio = \dfrac{ \dfrac{\pi \: r}{t} }{ \dfrac{2r}{t} } \\ \\ \implies \sf \: \frac{\pi \: rt}{2rt} \\ \\ \implies \sf \: \dfrac{\pi}{2}$

So, the ratio is π/2 .

★ Option A is correct.