Final answer:
The gravitational potential energy of a mass on a pendulum is calculated using the formula GPE = mgh, where h is the height it is lifted above its lowest point. Therefore, By calculating this height and then the GPE, the corresponding option of (b) 0.14mg is identified as the correct answer.
Step-by-step explanation:
The problem involves calculating the gravitational potential energy (GPE) of a mass supported by an ideal pendulum when the pendulum is displaced by an angle θ from the vertical. To find the GPE of the mass, you need to determine the vertical height h it was lifted.
The vertical height h can be calculated using the formula h = l - l\cos(\theta), where l is the length of the pendulum and θ is the angle with respect to the vertical. For a pendulum length of l = 1.1 m and an angle of θ = 21°, h will be:
h = 1.1 m - 1.1 m \cos(21°)
Once h is known, the GPE can be found with GPE = mgh, where g is the acceleration due to gravity (approx. 9.81 m/s²), and m is the mass of the pendulum bob. After calculating h and substituting the given values for m and g into the GPE formula, you can find the corresponding multiple of mg to match one of the given answer choices.
After calculations, the correct answer is (b) 0.14mg.