Question

A particle moves in a circular path of radius $R$ with an angular velocity $\omega =a-bt$, where $a$ and $b$ are positive constants and $t$ is time. The magnitude of the acceleration of the particle after time $\frac{2a}{b}$ is

• A. $\frac{a}{R}$
• B. $a^{2}R$
• C. $R\sqrt{a^4+b^2}$
• D. none of these

Answer 1

The correct option is C $R\sqrt{a^4+b^2}$

Angular acceleration $\alpha =\frac{d\omega }{dt}=-b$
$\Rightarrow$ Tangential acceleration $a_t=R\alpha =-Rb$
At $t=\frac{2a}{b},\omega =-a$
$\Rightarrow$ Centripetal acceleration $a_c=R{\omega }^2=R{a}^2$
Therefore, $a=\sqrt{a_t^2+a_n^2}=R\sqrt{a^4+b^2}$