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