Question

A particle moves along a circle of radius $\left(\frac{20}{\pi}\right) m$ with constant tangential acceleration. If the velocity of the particle is $80\, m/s$ at the end of the second revolution after motion has begun, the tangential acceleration is

• A. $40 \, m/s^2$
• B. $640 \, \pi \, m/s^2$
• C. $160 \, \pi \, m/s^2$
• D. $40\, \pi \, m/s^2$

Answer 1

Answer: (A)

$r=\frac{20}{\pi} m , v=80 \,m / s , \theta=2 \,rev =4 \,\pi \,rad$
From equation $\omega^{2}=\omega_{0}^{2}+2 \alpha \theta \left(\omega_{0}=0\right)$
$\omega^{2}=2 \alpha \theta\left(\omega=\frac{v}{r} \text { and } a=r \alpha\right) $
$a=\frac{v^{2}}{2 r \theta}=40\, m / s ^{2}$