Question

A boy whirls a ball on a string along a horizontal circle of radius 98 cm. The angular velocity (in rad $s^{-1}$) so that its centripetal acceleration has the same magnitude as $g$ is ________.

• A. $\sqrt{10}$
• B. $\frac{1}{\sqrt{10}}$
• C. 10
• D. 0.1
• E. 100

Hint:

$\omega = \sqrt{a/r}$.

Answer 1

The Correct Option is A

Step 1: Concept
Centripetal acceleration $a_c = r\omega^{2}$.

Step 2: Meaning
We are given $a_c = g = 9.8~ms^{-2}$ and $r = 98 \text{ cm} = 0.98 \text{ m}$.

Step 3: Analysis
$9.8 = 0.98 \times \omega^{2} \implies \omega^{2} = \frac{9.8}{0.98} = 10$.

Step 4: Conclusion
$\omega = \sqrt{10} \text{ rad } s^{-1}$. Final Answer: (A)