A pendulum of length L oscillates with an angular amplitude of θ = 60° and time period T. Let T0 = 2π√(L/g) be the time period for small angle of oscillations, where g is the acceleration due to gravity. If air resistance is negligibly small and the string remains straight, then which one of the following is correct?

The standard formula T0 = 2π√(L/g) is derived using the small-angle approximation, which assumes sin θ ≈ θ. This approximation is only accurate for small amplitudes (typically θ < 15°). For larger angles like θ = 60°, the restoring force is slightly less than what the linear approximation predicts, causing the pendulum to move slower and take more time to complete a cycle.

The exact period T is given by an infinite series: T = T0 [1 + (1/2)2 sin2(θ/2) + (3/8)2 sin4(θ/2) + ...]. Since the additional terms are positive, T will always be greater than T0 for any finite angle. For θ = 60°, T is approximately 7.3% greater than T0. Additionally, the period of a simple pendulum is independent of the mass of the bob, making option D incorrect.