Question

Consider an object making uniform motion around a circle of radius $5\, m$ with tangential velocity $2 \,ms ^{-1}$. The time it takes to complete $2$ revolution and the magnitude of acceleration respectively are

• A. $0.2\,{\pi} \,s$ and $0.8 \,ms ^{-2}$
• B. $0.5 \,\pi\, s$ and $1 \,ms ^{-2}$
• C. $10 \,\pi \,s$ and $0.8 \,ms ^{-2}$
• D. $5 \pi \,s$ and $5 \,ms ^{-2}$

Answer 1

Answer: (C)

Given that, circle of radius $=5\, m$
tangential velocity $=2 \,m / s$

Here, 2 revolutions complete by object.
$\because$ We know that,
$ v=\omega\, R $
$ \Rightarrow \, \frac{v}{R}=\omega $
$\Rightarrow \, \omega =\frac{2}{5} \,rad / s$
Also, $ \omega=\frac{2 \pi}{T}$
$ \Rightarrow \, T=\frac{2 \pi}{\omega}=\frac{2 \pi}{2 / 5}$
$T=5 \pi\, s$ for one revolution.
$\Rightarrow $ The body completes 2 revolutions in time,
$t=2 \times 5 \times \pi=10 \pi \,s$
Also acceleration, $\alpha=v^{2} / R=\frac{2^{2}}{5}=0.8 \,ms ^{-2}$