A particle revolving in circular path completes first one third of circumferences in 2 sec, while next one third 1s. Calculate the average angular velocity of particle?

Question

A particle revolving in circular path completes first one third of circumferences in 2 sec, while next one third 1s. Calculate the average angular velocity of particle? (A) (4 π/9) rad / s (B) (4 π/5) rad / s (C) (9 π/4) rad / s (D) (π/4) rad / s

Tardigrade Admin · Accepted Answer

θ1=(2 π/3) and θ2=(2 π/3) Total time T =2+1=3 s ∴ < Wa v > =(θ1+θ2/T) =((2 π/3)+(2 π/3)/3)=(3/3) =(4 π/9) rad / s

Q. A particle revolving in circular path completes first one third of circumferences in $2 sec$ , while next one third 1s. Calculate the average angular velocity of particle?

$\frac{4 π}{9} r a d / s$

$\frac{4 π}{5} r a d / s$

$\frac{9 π}{4}$ rad $/ s$

$\frac{π}{4} r a d / s$

$θ_{1} = \frac{2 π}{3}$ and $θ_{2} = \frac{2 π}{3}$
Total time $T = 2 + 1 = 3 s$
$∴ < W_{a v} >= \frac{θ _{1} + θ _{2}}{T}$
$= \frac{\frac{2 π}{3} + \frac{2 π}{3}}{3} = \frac{3}{3}$
$= \frac{4 π}{9} r a d / s$

Q. A particle revolving in circular path completes first one third of circumferences in 2sec, while next one third 1s. Calculate the average angular velocity of particle?

94π​rad/s

54π​rad/s

49π​ rad /s

4π​rad/s