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A body rotates about a fixed axis with an angular acceleration $$1  rad/s^{2}$$. The angle (in radians), it rotates during the time in which its angular velocity increases from $$ 5  rad/s $$ to $$15  rad/s$$ is given by $$10^x$$. Then $$x$$ is : 


Solution

$$ \omega ^{2}=\omega _{0}^{2} +2 \alpha \theta$$

$$\displaystyle \therefore \theta =\frac{ \omega^{2}-\omega_{0}^{2}}{2\alpha} =\frac{225-25}{2\times 1}$$

$$=100\: rad$$

Physics

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