​ A string of length L is fixed at one end and carries a mass of M at the other end. The mass makes 3 / π

Question

 

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

Answer 1

Answer is : 36

 

\(T \cos\theta = mg\ ..(1)\)

\(T\sin \theta = M\omega^2R\ ...(2)\) 

Using equation (2)

\(T\sin\theta = M\omega ^2(L\sin \theta)\) 

\(T = M\omega ^2 L = M\left(\frac{3}{\pi} \times 2 \pi\right)^2\ L\) 

\(T = 36\ ML\)