Question

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

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

Answer 1

Answer: (D)

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