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

Step-by-step solution

Conical pendulum analysis The mass experiences tension T along the string and gravitational force mg downward. Resolving tension into components: vertical component T balances gravity, giving T = mg . The horizontal component T provides centripetal force for circular motion with radius r = l . Given frequency f = 1 , angular frequency becomes = 2 f = 2 rad/s. Centripetal force is F_c = m ^2 r = m(2)^2(l ) = 4ml . Equating horizontal forces: T = 4ml . Since 0 , dividing yields T = 4ml . 4ml