Question

A particle moves in a circle of radius $30 \, cm$ . 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. $220 \, m \, s^{- 2},50 \, m \, s^{- 2}$
• B. $100 \, m \, s^{- 2},5 \, m \, s^{- 2}$
• C. $120 \, m \, s^{- 2},2 \, m \, s^{- 2}$
• D. $110 \, m \, s^{- 2},10 \, m \, s^{- 2}$

Answer 1

Answer: (C)

Given that, the radius of the circle, $r=30cm=0.3m$
$linear \, speed \, v=2t$
$Now, \, radial \, acceleration \, a_{R}=\frac{v^{2}}{r}=\frac{\left(2 t\right)^{2}}{0.3}$
$at \, \, t=3s$
$a_{R}=\frac{\left(2 \times 3\right)^{2}}{0.3}$
$\frac{36}{0.3}=120m s^{- 2}$
$or \, \, a_{R}=120m s^{- 2}$
$and \, tangential \, acceleration \, a_{T}=\frac{d v}{d t}=\frac{d}{d t}\left(2 t\right)=2\left(m s\right)^{- 2}$