Question

A particle moves in a circle of radius $5 \,cm$ with constant speed and time period $0.2 \,\pi\, s$. The acceleration of the particle is

• A. $15 \,m/s^2 $
• B. $25 \,m/s^2 $
• C. $36 \,m/s^2 $
• D. $5 \, m/s^2 $

Answer 1

Answer: (D)

Here, Radius, $R=5 cm =5 \times 10^{-2}\,m$
Time period, $T=0.2 \pi s$
Centripetal acceleration
$a_{c}=\omega^{2} R=\left(\frac{2 \pi}{T}\right)^{2} R=\left(\frac{2 \pi}{0.2 \pi}\right)^{2}\left(5 \times 10^{-2}\right)=5\, m / s ^{2}$
As particle moves with constant speed, therefore its tangential acceleration is zero.
So, $a_{t}=0$
The acceleration of the particle is
$a=\sqrt{a_{c}^{2}+a_{t}^{2}}=a_{c}=5\, m / s ^{2}$