A string of length 'L' fixed at one end carries a mass 'm' at the other end. The string makes 3 r.p.s. around the vertical axis through fixed end. The tension in the string is

Step-by-step solution

For a mass rotating in a horizontal circle as a conical pendulum, the horizontal component of the tension provides the necessary centripetal force. T = m ^2 r From the geometry of the pendulum, the radius of the circular path is r = L . Substituting this into the equation gives: T = m ^2 (L ) T = m ^2 L The frequency of revolution is given as f = 3 . The angular velocity is: = 2 f = 2 ( 3 ) = 6 Substituting the value of into the expression for tension: T = m (6)^2 L = 36 mL Answer: 36 mL