Question

A particle moves in a circle of radius $30\, cm$. Its linear speed is given by: $V =2 t$, 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. $110 \, m / \sec ^2, 5 \, m / \sec ^2$
• C. $120 \, m / \sec ^2, 2\, m / \sec ^2$
• D. $110 \, m / \sec ^2, 10 \, m / \sec ^2$

Answer 1

Answer: (C)

Given : $r =30 \,cm =0.3 \,cm =0.3 \,m$ and $V =2 t$
Radial acceleration at $t =3 \sec$
$a_r=\frac{v^2}{r}=\frac{4 t^2}{0.3}=\frac{4 \times(3)^2}{0.3}=120 \, m / s ^2$
and tangential acceleration
$a_t=\frac{d v}{d t}=2 \,m / s ^2$