Final answer:
The work done on the pendulum is calculated by finding the change in gravitational potential energy as the bob is raised to a height determined by using trigonometry and the given angle.
Step-by-step explanation:
The student has asked about determining the work done on a pendulum bob of mass 0.1 kg when it is pulled until the string makes an angle of 30° with the vertical. To find the work done, one must consider the change in gravitational potential energy of the pendulum bob when it is raised to the initial height. Using trigonometry, the vertical height (h) the bob is raised can be calculated as h = L - L \( \cos(\theta) \), where L is the length of the string (1 m), and \( \theta \) is the angle (30°).
The gravitational potential energy at height h is given by U = mgh, where m is the mass of the bob, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height. The work done equals the change in potential energy, which is the potential energy at height h minus the potential energy at the lowest point (which is zero since height is zero).
Thus, the work done to pull the pendulum bob up to the initial height is W = mgL(1 - \( \cos(\theta) \)), and substituting the given values gives the numerical result for work done on the pendulum bob.