Question

The angular turned by a body undergoing circular motion depends on time as $\theta ={\theta }_0+{\theta }_1{t}^2$, the ratio of angular acceleration and initial angular velocity is

• A. $\frac{2{\theta }_2}{{\theta }_1}$
• B. $\frac{{\theta }_2}{{\theta }_1}$
• C. $\frac{2{\theta }_1}{{\theta }_2}$
• D. $\frac{{\theta }_1}{{\theta }_2}$

Answer 1

The correct option is A $\frac{2{\theta }_2}{{\theta }_1}$

Given that,

$\theta ={\theta }_0+{\theta }_{1}t+{\theta }_2{t}^2$

Angular velocity $\omega =\frac{d\theta }{dt}={\theta }_1+2{\theta }_{2}t$

Angular acceleration $\alpha =\frac{d\omega }{dt}=2{\theta }_2......\left(1\right)$

At t = 0 s angular velocity is $\omega ={\theta }_1........\left(2\right)$

Taking ratios of angular acceleration and initial angular velocity

$\frac{2{\theta }_2}{{\theta }_1}$