A ball of mass 0 . 5 kg is attached to a string of length 50 cm . The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is 400 N . The maximum possible value of angular velocity of the ball in rad s - 1 is,:

Step-by-step solution

Let the string makes angle θ with the vertical. Weight will be balanced by the vertical component of tension, which is T cos θ = m g and the horizontal component towards the centre will provide the required centripetal force for circular motion. Therefore, T sin θ = m ω 2 l sin θ , where l = length of the string. ⇒ 400 sin θ = 0 .5 ω 2 × 0 .5 sin θ ⇒ ω = 40 rad s - 1