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)

$5 \, m/s^2$

Answer 2

If particle move in a circular path with constant speed, the acceleration of the particle is centripetal acceleration
$a _{ c }=\omega^{2} R =\left(\frac{2 \pi}{ T }\right)^{2}\, R$
$a _{ c }=\frac{4 \pi^{2} R }{ T ^{2}}=\frac{4 \pi^{2}}{(0.2 \pi)^{2}} \times 5 \times 10^{-2}$
$a _{ c }=5 \,m / \,sec ^{2}$