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Length of a simple pendulum is I and its maximum angular displacement is θ then its maximum K.E. is :

Length of a simple pendulum is I and its maximum angular displacement is θ then its maximum K.E. is : Correct Answer mgl(1−cosθ)

CONCEPT:

Work-Energy Theorem: 

  • The work-energy theorem states that the net work done by the forces on an object is equal to the change in its kinetic energy.

​⇒ W = ΔKE     -----(1)

Where W = work done and ΔKE = change in kinetic energy

​CALCULATION:

Given l = length of the pendulum and θ = maximum angular displacement

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⇒ At maximum displacement, the KE = 0 J, and maximum KE will occur at the lowest point when θ = 0.

So,

⇒ ΔKE = KE2 - KE1 = KE2 - 0 = Maximum KE

By equation 1,

⇒ Maximum KE = W

From the above diagram, it is clear that the pendulum will do work done due to the gravitational force.

⇒ Maximum KE = mg(l - lcosθ) = mgl(1 - cosθ)

  • Hence, option 4 is correct.

Related Questions

If the amplitude or oscillation of a simple pendulum is very small, then its time period of oscillation
1. depends on the length of the pendulum, L.
2. depends on the acceleration due to gravity, g.
3. depends upon the mass of the bob of the pendulum, m.
4. does not depend upon the amplitude of the pendulum, A.
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