A particle is moving with constant speed in a circular path. When the particle turns by an angle 90°, the ratio of instantaneous velocity to its average velocity is . The value of will be [2023]

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Solution

Q.
A particle is moving with constant speed in a circular path. When the particle turns by an angle 90°, the ratio of instantaneous velocity to its average velocity is $π : x \sqrt{2}$ . The value of $x$ will be [2023]

1 1

2 2

3 7

4 5

Ans.
(2)

$A B = R \sqrt{2}$

Let instantaneous velocity be $v$ , time,

$t = \frac{Arc length}{v} = \frac{2 π \frac{R}{4}}{v} = \frac{π R}{2 v}$

Average velocity, $< v > = \frac{A B}{t} = \frac{R \sqrt{2} (2 v)}{π R} = \frac{2 \sqrt{2} v}{π}$

$\Rightarrow \frac{v}{⟨ v ⟩} = \frac{π}{2 \sqrt{2}}$

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