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  • As shown in the figure, a particle is moving with constant speed m/s. Considering its motion from A to B, the

As shown in the figure, a particle is moving with constant speed \pim/s. Considering its motion from A to B, the

magnitude of the average velocity is :

                                   

Option: 1

\pi  m / s


Option: 2

2\sqrt3   m / s 


Option: 3

\sqrt3  m /s


Option: 4

1.5\sqrt3  m /s


Answers (1)

best_answer

Given speed v = \pi m/s

\begin{aligned} or\, \, & \mathrm{R} \omega=\pi \\ or\, \, \, & \omega=\frac{\pi}{\mathrm{R}} \mathrm{rad} / \mathrm{s} \end{aligned} 

angular displacement \theta = 120°  or  \frac{2\pi}{3}

uising   \theta=\omega t\\

\mathrm{t}=\frac{\theta}{\omega}=\frac{2 \pi / 3}{\pi / R}=\frac{2 \mathrm{R}}{3}

linear displacement d = 2 R sin (\theta / 2) 

\begin{aligned} &\begin{aligned} & d=2 R \sin \left(\frac{120}{2}\right) \\ & =2 R \times \sin 60=2 R \times \frac{\sqrt{3}}{2} \\ & =R \sqrt{3} \end{aligned}\\ &\text { average velocity }=\frac{\mathrm{d}}{\mathrm{t}}=\frac{\mathrm{R} \sqrt{3}}{2 \mathrm{R} / 3}=\frac{3 \sqrt{3}}{2} \end{aligned}

 

 

Posted by

Nehul

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