A particle undergoes uniform circular motion The velocity and angular velocity of the particle at an instant of time is $v = 3 \hat{i} + 4 \hat{j} m / s$ and $\vec{ω} = x \hat{i} + y \hat{j} m / s$ then

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The value of x in rad/s is -4

The radius of circle in meters is 1

The acceleration of particle at the given instant is ${25m/s}^{2}$

The radius of circle in meters is 0.5

answer is A.

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Detailed Solution

$\vec{V} . \vec{ω} = 0$

$3 x + 12 = 0$

$3 x = - 12$

$x = - 4$

$V = \sqrt{9 + 16} = 5 m / s$

$ω = \sqrt{16 + 9} = 5 r a d / s$

$r = \frac{V}{ω} = 1 m$

$a = \frac{V^{2}}{r} = \frac{25}{1} = 25 m / s^{2}$

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