The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10 m . If it dissipates 10 % of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is: [Use, g = 10 m s - 2 ]

Step-by-step solution

Given the length of the pendulum is ℓ = 10 m . The initial potential energy of the pendulum at the horizontal position is given by U = m g ℓ . . . 1 The final kinetic energy of the pendulum at the lowermost position is given by K = 1 2 m v 2 . . . 2 So, from equations (1) and (2), it follows that 9 10 m g ℓ = 1 2 m v 2 ⇒ 9 10 × 10 × 10 = 1 2 v 2 ⇒ v 2 = 180 ⇒ v = 180 = 6 5 m s - 1