Q. A particle moves in a circle of radius 30cm. Its liner speed is given by $v = 2t,$ where $t$ is in second and $v$ in ${ms}^{- 1}$. Find out its, radial and tangential acceleration at $t = 3s$, respectively,
A) $220\ {ms}^{- 2},50\ {ms}^{- 2}$
B) $100\ {ms}^{- 2},5\ {ms}^{- 2}$
C) $120\ {ms}^{- 2},2\ {ms}^{- 2}$
D) $110\ {ms}^{- 2},10\ {ms}^{- 2}$
Explanation
(c) Given that, radius of circle, $r = 30cm = 0.3m$
$linear\ speed\ v = 2t$
$Now,\ radial\ acceleration\ a_{R} = \frac{v^{2}}{r} = \frac{(2t)^{2}}{0.3}$
$at\ \ t = 3s$
$a_{R} = \frac{(2 \times 3)^{2}}{0.3}$
$\frac{36}{0.3} = 120{ms}^{- 2}$
$or\ \ a_{R} = 120{ms}^{- 2}$
$and\ tangential\ acceleration\ a_{T} = \frac{dv}{dt} = \frac{d}{dt}(2t) = 2{ms}^{- 2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.