The time period (T) of a simple pendulum is given by the formula T = 2π√(l/g), where l is the length of the string and g is the acceleration due to gravity. This formula shows that the time period depends only on the length of the pendulum and the acceleration due to gravity, and it is independent of the mass of the bob. In the given problem, the initial time period is T for a pendulum with mass m and length l. When the mass of the bob is doubled (to 2m) and the length of the string is halved (to l/2), the new time period T' will be T' = 2π√((l/2)/g) = 2π√(l/(2g)). We can rewrite this as T' = 2π√(l/g) (1/ √2). Since T = 2π√(l/g), the new time period T' is T/ √2.
A simple pendulum having bob of mass m and length of string l has time period of T. If the mass of the bob is doubled and the length of the string is halved, then the time period of this pendulum will be
Asked in UPSC NDA 2 2022 · Topic: Mechanics (Simple Harmonic Motion and Damped/Forced Oscillations)
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