Question 158: Work, Energy and Power & Circular Motion

Question

A string of length $L$ is fixed at one end and carries a mass of $M$ at the other end. The mass makes $\left(\frac{3}{\pi}\right)$ rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is __________ ML.

Accepted Answer

$$\begin{aligned}
& \mathrm{T} \cos 	heta=\mathrm{mg} \
& \mathrm{~T} \sin 	heta=\mathrm{M} \omega^2 \mathrm{R} \
& 	ext { Using equation (2) } \
& \mathrm{T} \sin 	heta=\mathrm{M} \omega^2(\mathrm{~L} \sin 	heta) \
& \mathrm{T}=\mathrm{M} \omega^2 \mathrm{~L}=\mathrm{M}\left(\frac{3}{\pi} 	imes 2 \piight)^2 \mathrm{~L} \
& \mathrm{~T}=36 \mathrm{ML}
\end{aligned}$$

Work, Energy and Power & Circular Motion

A string of length L is fixed at one end and carries a mass of M at the other end. The mass makes \left(\frac{3}{\pi}\right) rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is __________ ML.

Integer / Numeric Answer Type