Question

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 $m{s}^{-1}$ . Find out its radial and tangential acceleration at $t=3s$ , respectively,

• A. $220m{s}^{-2},50m{s}^{-2}$
• B. $100m{s}^{-2},5m{s}^{-2}$
• C. $120m{s}^{-2},2m{s}^{-2}$
• D. $110m{s}^{-2},10m{s}^{-2}$

Answer 1

Answer: (C)

Given that, the radius of the circle, $r=30cm=0.3m$
$linearspeedv=2t$
$Now,radialacceleration{a}_R=\frac{v^2}{r}=\frac{{\left(2t\right)}^2}{0.3}$
$att=3s$
$a_R=\frac{{\left(2\times 3\right)}^2}{0.3}$
$\frac{36}{0.3}=120m{s}^{-2}$
$or{a}_R=120m{s}^{-2}$
$andtangentialacceleration{a}_T=\frac{dv}{dt}=\frac{d}{dt}\left(2t\right)=2{\left(ms\right)}^{-2}$