A particle P starts from rest with constant angular acceleration α in anti-clockwise direction from point P…..

Q: A particle P starts from rest with constant angular acceleration α in anti-clockwise direction from point P on a circular path of radius R. The acceleration of the particle at , $ \displaystyle t = \sqrt{ \frac{\pi}{\alpha}}$ is

Numerical

(a) $ \displaystyle R \alpha \hat{i} + \pi R \alpha \hat{j}$ is

(b) $ \displaystyle R \alpha \hat{k} + \pi R \alpha \hat{j}$ is

(c) $ \displaystyle -R \alpha \hat{i} – \pi R \alpha \hat{j}$ is

(d) None of these

Ans: (c)

Sol: $ \displaystyle \theta = \omega_0 t + \frac{1}{2}\alpha t^2 $

$\displaystyle \omega = \alpha t = \alpha \sqrt{\pi/\alpha} = \sqrt{\pi \alpha} $

$ \displaystyle \theta = 0 + \frac{1}{2}\alpha \times \frac{\pi}{\alpha} = \pi/2 $

Centripetal acceleration , $ \displaystyle a_r = \omega^2 R = \pi \alpha R $

$ \displaystyle \vec{a} = -a_t\hat{i}- a_r\hat{j} $

$ \displaystyle \vec{a} = -\alpha R\hat{i}-\pi R\alpha\hat{j} $

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