Question

A particle moves with constant speed along a circle. The modulus of average acceleration in covering an angle $\theta$ is $a_1$ and in covering an angle $2\pi +\theta is{a}_2.$ If $\frac{a_1}{a_2}=4$ and if the value of $\theta$ (in degree) is $15\alpha .$ Then $\alpha$ will be

Answer 1

In covering angle $\theta$ and $2\pi +\theta$ ,the change in velocity is the

same. Therefore the accelerations is inversely proportional to the time.

so, $\frac{a_1}{a_2}=\frac{T+t}{t}$ where t is the time taken cover angle $\theta$ and T is the taken time for covering $2\pi$.

or $4=\frac{T+t}{t}$

or $4t=T+t\Rightarrow t=T/3$

$\Rightarrow \theta =\frac{2\pi }{3}rad=\frac{2\pi }{3}\times \frac{180}{\pi }$ degree

or $\theta ={120}^o=15\alpha$

$\Rightarrow \alpha =8$