# 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

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

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

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