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3.2 , motion in plane — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics3.2 , motion in plane1 Mark
MCQ
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 $.........$
  • ✓
    $2$
  • B
    $5$
  • C
    $1$
  • D
    $7$
✓

Answer

Correct option: A.
$2$
a
Let instantaneous velocity be v. time,

$t =\frac{\text { Arc length }}{ v }=\frac{2 \pi \frac{ R }{4}}{ v }=\frac{\pi R }{2 v }$ average velocity,

$\langle v \rangle =\frac{ AB }{ t }=\frac{ R \sqrt{2}(2 v )}{\pi R }=\frac{2 \sqrt{2} V }{\pi}$

$\Rightarrow \frac{ V }{\langle V \rangle} =\frac{\pi}{2 \sqrt{2}} .$

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