Answer:
d. 2T
Step-by-step explanation:
Period of a simple pendulum: This can be defined as the time taken for a simple pendulum to complete an oscillation.
The S.I unit of the period of a simple pendulum is second (s).
Mathematically the period of a simple pendulum can be represented as
T = 2π√(L/g)................................................ Equation 1
Where T = period of the pendulum, L = length of the pendulum, g = acceleration due to gravity, π = pie.
Note: If the length of a simple pendulum is increased, the period will also increase, while acceleration due to gravity is constant.
Hence,
T' = 2π√(4L/g) ........................... Equation 2
Where T' is the new period when the length of the pendulum is increased by 4 time its original length.
Dividing equation 1 by equation 2
T/T' = 2π√(L/g)/2π√(4L/g)
T/T' = √L/2√L
T/T' = 1/2
T' = 2T
Thus, the right option is d. 2T