Looking for classes? Ksquare Career Institute, Bengaluru →
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
5 m/$s^2$
B
15 m/$s^2$
C
25 m/$s^2$
D
36 m/$s^2$
Detailed Solution
R = 5 cm = $5\times10^{-2}$ m, T = $0.2\pi$ s.
Angular speed $\omega = \frac{2\pi}{T} = \frac{2\pi}{0.2\pi} = 10$ rad/s
For constant speed the only acceleration is centripetal: $a = \omega^2R$
$a = (10)^2\times5\times10^{-2} = 100\times0.05$
a = 5 m/$s^2$
Angular speed $\omega = \frac{2\pi}{T} = \frac{2\pi}{0.2\pi} = 10$ rad/s
For constant speed the only acceleration is centripetal: $a = \omega^2R$
$a = (10)^2\times5\times10^{-2} = 100\times0.05$
a = 5 m/$s^2$