The bob of mass m of a resting pendulum is given a sharp hit, imparting a horizontal velocity of 10 ,gl , where l represents the pendulum's length. Determine the tension in the string when the string is horizontal.

Step-by-step solution

Let the initial velocity at the lowest point be v₀ = 10gl . Using the principle of conservation of mechanical energy between the lowest point and the horizontal position: 1 2 mv₀^2 = 1 2 mv^2 + mgl Substituting the value of v₀ : 1 2 m(10gl) = 1 2 mv^2 + mgl 5mgl - mgl = 1 2 mv^2 v^2 = 8gl At the horizontal position, the tension in the string provides the necessary centripetal force. The weight of the bob acts vertically downwards and has no component along the horizontal string. T = mv^2 l Substituting v^2 = 8gl :