A pendulum consists of a mass m suspended from a string of length L.When the pendulum is swinging,how much greater is the mass's potential energy when the string is displaced from the vertical by the angle θ than when the mass is at the lowest position?
A)mgLsinθ
B)mgLcosθ
C)mgL(1 - sinθ)
D)mgL(1 - cosθ)

Question

A pendulum consists of a mass m suspended from a string of length L.When the pendulum is swinging,how much greater is the mass's potential energy when the string is displaced from the vertical by the angle θ than when the mass is at the lowest position?
A)mgL​sinθ
B)mgL​cosθ
C)mgL(1 - sinθ)
D)mgL(1 - cosθ)

Quizplus · Accepted Answer

At the lowest position of the pendulum, the potential energy of the mass is given by:
PE = mgh
where h is the height of the mass from the lowest position, which is equal to L.

When the string is displaced from the vertical by an angle θ, the potential energy of the mass is given by:
PE = mgh'
where h' is the new height of the mass from the lowest position. Using trigonometry, we can find that:
h' = L(1-cosθ)

Substituting this value in the above equation for PE, we get:
PE = mgL(1-cosθ)

Therefore, the mass's potential energy is greater by mgL(1- cosθ) when the string is displaced from the vertical by the angle θ. Thus, the correct answer is D.

A Pendulum Consists of a Mass M Suspended from a String