Work, Energy and Power NCERT Solutions Class 11 Physics - Solved Exercise Question 6.18

Question 6.18:

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?

Solution:

Length of the pendulum, l = 1.5 m
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, E_P = mgl
Kinetic energy of the bob, E_K = 0
Total energy = mgl … (i)
At the lowermost point (mean position):
Potential energy of the bob, E_P = 0
Kinetic energy of the bob, E_K = (1/2)mv²
Total energy E_x = (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) mgl
∴  v = (2 X 95 X 1.5 X 9.8 / 100)^1/2
= 5.28 m/s