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
T
T /√2
2T
√2 T
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC NDA-2 – 2022
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.