NCERT Solutions
Class 11 Physics
Work Energy and Power

Q. 5.18
The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?
Given:
Length of the pendulum l =1.5m
Mass of the bob = m
Energy dissipated = 5%
According to the law of conservation of energy, the total energy of the system remains constant.
At the horizontal position:
Potential energy of the bob, EP = mgl
Kinetic energy of the bob, EK = 0
Total energy = mgl ... (i)
At the lowermost point (mean position):
Potential energy of the bob, EP = 0
Kinetic energy of the bob, Ek = (1/2) mv2
Total energy = ET = (1/2) mv2... (ii)
As the bob moves from the horizontal position to the lowermost point, 5% of its energy gets dissipated.
The total energy at the lowermost point is equal to 95% of the total energy at the horizontal point, i.e.
(1/2) mv2 = (95/100) x mgl
v = √ (2x95x1.5x9.8)/ (100)
=5.285m/s