A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first $2\ sec$, it rotates through an angle $ heta_{1}$. In the next $2\ sec$, it rotates through an additional angle $ heta_{2}$. The ratio of $ heta_{2}\ / heta_{1}$ is

Question

A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first $2\ sec$, it rotates through an angle $	heta_{1}$. In the next $2\ sec$, it rotates through an additional angle $	heta_{2}$. The ratio of $	heta_{2}\ /	heta_{1}$ is

Dr. Abubacker · Accepted Answer

(c) Using relation $	heta = \omega_{0}t + \frac{1}{2}at^{2}$
$	heta_{1} = \frac{1}{2}(\alpha)(2)^{2} = 2\alpha$ …(i)
As $\omega_{0} = 0,\ t = 2\ sec$
Now using same equation for $t = 4\ sec,\ \omega_{0} = 0$
$	heta_{1} + 	heta_{2} = \frac{1}{2}\alpha(4)^{2} = 8\alpha$ …(ii)
From (i) and (ii), $	heta_{1} = 2\alpha$ and $	heta_{2} = 6\alpha\ 	herefore\frac{	heta_{2}}{	heta_{1}} = 3$

Q. A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first $2\ sec$, it rotates through an angle $\theta_{1}$. In the next $2\ sec$, it rotates through an additional angle $\theta_{2}$. The ratio of $\theta_{2}\ /\theta_{1}$ is

Explanation

Reviewed by Dr. Abubacker

Want more practice?