The bob of a stationary pendulum receives a sharp hit, imparting to it a horizontal speed of 3gl . Determine the angle rotated by the string before it becomes slack.

Step-by-step solution

Let the angle rotated by the string from the lowest point be and the velocity of the bob at this position be v . Using the principle of conservation of mechanical energy between the lowest point and the position at angle : 1 2 mv₀^2 = 1 2 mv^2 + mgl(1 - ) Given v₀ = 3gl , substituting this into the equation: 1 2 m(3gl) = 1 2 mv^2 + mgl(1 - ) v^2 = 3gl - 2gl(1 - ) = gl(1 + 2 ) The equation of motion for the bob along the radial direction is: T - mg = mv^2 l Substituting the expression for v^2 : T = mg + m l [gl(1 +