A bob of a simple pendulum has a speed of 3 m/s at its lowest position. The pendulum is 0.5 m long. The speed of the bob, when the length makes an angle of (60)^ with the vertical, is (Take g = 10 m/s ^2 , 60^ = 1/2 )

Step-by-step solution

Let the lowest position be the reference level for potential energy. At the lowest position, the total mechanical energy is purely kinetic: E_i = 1 2 m v₀^2 When the pendulum makes an angle with the vertical, the height of the bob above the lowest position is: h = L - L = L(1 - ) At this position, the total mechanical energy is the sum of kinetic and potential energy: E_f = 1 2 m v^2 + mgh By conservation of mechanical energy: 1 2 m v₀^2 = 1 2 m v^2 + mgh v^2 = v₀^2 - 2gh Substituting h = L(1 - ) : v^2 = v₀^2 - 2gL