Question 173: Work, Energy and Power & Circular Motion

Question

An inextensible string of length ' $l$ ' fixed at one end, carries a mass ' $m$ ' at the other end. If the string makes $\frac{1}{\pi}$ revolutions per second around the vertical axis through the fixed end, the tension in the string is [The string makes an angle $	heta$ with the vertical]

Accepted Answer

$$ \begin{aligned} &	ext { Given that, } \mathrm{f}=\frac{1}{\pi} \mathrm{rps} 	ext {, }\ &	herefore \quad \omega=2 \pi \mathrm{f}=2 \pi 	imes \frac{1}{\pi}=2 \mathrm{rad} / \mathrm{s} \end{aligned} $$
The centripetal force is provided by the horizontal component of the tension i.e., ( $\mathrm{T} \sin 	heta$ ).
$$ \begin{array}{ll} 	herefore & 	ext { Tsin } 	heta=m r \omega^2 \ & 	ext { But } r=l \sin 	heta 	ext { and } \ & \omega^2=4 \ 	herefore & T \sin 	heta=m 	imes(l \sin 	heta) 	imes 4 \ 	herefore & T=4 m l \end{array} $$

Answer

16 ml

Answer

8 ml

Answer

4 ml

Answer

2 ml

Work, Energy and Power & Circular Motion

An inextensible string of length ' l ' fixed at one end, carries a mass ' m ' at the other end. If the string makes \frac{1}{\pi} revolutions per second around the vertical axis through the fixed end, the tension in the string is [The string makes an angle \theta with the vertical]

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