Question

A weightless thread can bear tension upto 37 N. A stone of mass 500 g is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If $ g=10\,\text{m}{{\text{s}}^{-2}}, $ then the maximum angular velocity of the stone will be:

• A. $ 2\,\text{rad}\,{{s}^{-1}} $
• B. $ 4\,\text{rad}\,{{s}^{-1}} $
• C. $ 8\,\text{rad}\,{{s}^{-1}} $
• D. $ 16\,\text{rad}\,{{s}^{-1}} $

Answer 1

Answer: (B)

Maximum tension in the thread is given by $ {{T}_{\max }}=mg+\frac{m{{v}^{2}}}{r} $ or $ {{T}_{max}}=mg+mr{{\omega }^{2}}(\because \,v=r\omega ) $ or $ {{\omega }^{2}}=\frac{{{T}_{\max }}-mg}{mr} $ Given, $ {{T}_{\max }}=37\,N,\,m=500g=0.5kg,\,g=10\,m{{s}^{-2}}, $ $ r=4\,m $ $ \therefore $ $ {{\omega }^{2}}=\frac{37-0.5\times 10}{0.5\times 4}=\frac{37-5}{2} $ or $ {{\omega }^{2}}=16 $ or $ \omega =4\,rad\,{{s}^{-1}} $