Question 71: Work, Energy and Power & Circular Motion

Question

A particle is moving with constant speed in a circular path. When the particle turns by an angle $$90^{\circ}$$, the ratio of instantaneous velocity to its average velocity is $$\pi: x \sqrt{2}$$. The value of $$x$$ will be -

Accepted Answer

$$
\begin{aligned}
& 	ext { Instantaneous velocity }=\omega R \\
& 	ext { Time taken }=\frac{\pi}{2 \omega} \\
& 	ext { Displacement }=R \sqrt{2} \\
& 	ext { Average velocity }=\frac{R \sqrt{2} 	imes 2 \omega}{\pi}=\frac{2 \sqrt{2}}{\pi} \omega R \\
& \Rightarrow \frac{v_{	ext {ins }}}{v_{	ext {avg }}}=\frac{\omega R \pi}{2 \sqrt{2} \omega R} \\
& \Rightarrow x=2
\end{aligned}
$$

Answer

1

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7

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5

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2

Work, Energy and Power & Circular Motion

A particle is moving with constant speed in a circular path. When the particle turns by an angle $90^{\circ}, the ratio of instantaneous velocity to its average velocity is \pi: x \sqrt{2}. The value of x$ will be -

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