Question

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

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

Answer 1

Answer: (C)

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

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, $\alpha =v^2/R=\frac{2^2}{5}=0.8m{s}^{-2}$