Question

A particle is moving with constant angular acceleration \(4\,\text{rad/s}^2\) in circular path. At what time the magnitudes of its tangential acceleration and centripetal acceleration will be equal ?

• A. \(0.2\) s
• B. \(0.4\) s
• C. \(0.5\) s
• D. \(0.6\) s

Hint:

Tangential is r alpha, centripetal is omega squared r with omega = alpha t.

Answer 1

The Correct Option is C

Step 1: Ratio method:
$\dfrac{a_c}{a_t} = \dfrac{\omega^2r}{\alpha r} = \dfrac{\alpha^2t^2}{\alpha} = \alpha t^2$.

Step 2: Equal means ratio 1:
$\alpha t^2 = 1$, so $t^2 = \dfrac14$.

Step 3: Result:
$t = 0.5$ s, option (C), assuming the particle starts from rest.

Final Answer:
The two accelerations are equal at 0.5 s. \[ \boxed{\text{(C) }0.5\ \text{s}} \]