Work, Energy and Power

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]

1. 5 6 m s-1
2. 5 5 m s-1
3. 2 5 m s-1
4. 6 5 m s-1

Answer

(4) 6 5 m s-1

Solution

Initial energy (w.r.t. lowest point): E=mgl

90% of E is left at the lowest point:

12mv2= 910mgl

v2=2 910 10 10=180

v= 180=6 5 m s-1

The bob falls through a height equal to the length l; 10% of this energy is lost.

Answer: (4)