Question

A rod of length l is clamped to axis of rotation. A string of length l is tied at one end and a mass m at the other as shown. Find angular velocity such that the string makes an angle q with vertical –

• A. $\sqrt{\frac{g\tan\theta}{\mathcal{l–l}sin\theta}}$
• B. $\sqrt{\frac{g\tan\theta}{\mathcal{l} + \mathcal{l}\sin\theta}}$
• C. $\sqrt{\frac{g\tan\theta}{\mathcal{l + l}\cos\theta}}$
• D. $\sqrt{\frac{g\tan\theta}{\mathcal{l–l}\cos\theta}}$

Answer 1

Answer: (B)

$\sqrt{\frac{g\tan\theta}{\mathcal{l} + \mathcal{l}\sin\theta}}$

Answer 2

T cos q = mg

T sin q = mw² = (l + l sin q)

\ tan q = $\frac{\omega^{2}\mathcal{l}(1 + \sin\theta)}{g}$

w = $\sqrt{\frac{g\tan\theta}{\mathcal{l} + \mathcal{l}sin\theta}}$