A particle starting from rest, moves in a circle of radius ‘r’. It attains a velocity of V₀ m/s in the n^thround. Its angular acceleration will be

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$\frac{V_{0}}{n} rad / s^{2}$

$\frac{V_{0}^{2}}{2 π {nr}^{2}} rad / s^{2}$

$\frac{V_{0}^{2}}{4 π {nr}^{2}} rad / s^{2}$

$\frac{V_{0}^{2}}{4 πnr} rad / s^{2}$

answer is C.

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Detailed Solution

Initial speed = 0; Final speed = V₀
Tangential acceleration $= α_{t}$
$\begin{array}{l} V^{2} = u^{2} + 2 as; \\ V_{0}^{2} = 0 + 2 r a_{t} (2 πr) n \\ a_{t} = \frac{V_{0}^{2}}{4 π {nr}^{2}} \end{array}$

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