A simple pendulum has a period of 17.0s. When the length is shorten by 1.5m,…

A simple pendulum has a period of 17.0s. When the length is shorten by 1.5m, its period is 8.5s. Calculate the original length of the pendulum
  • A.
    4.0 m
  • B.
    3.0 m
  • C.
    2.0 m
  • D.
    1.5 m
Correct Answer: Option C
Explanation

For a simple pendulum, the period T = 2π
√  1/g 
Since g, 2 and π are constant, => T ∝ √l
∴ T = K√l
Let the original length = l
thus for the length l, period T = 17s
∴ 17 = K√1 ……………… [1] Again, for the new length [1 – 1.5] the period T = 8.5s∴ 8.5 = k
√ [1-1.5] ……………[2]
thus dividing eqn [1] by eqn[2] we have 17/8.5 = √(l/l-1.5)
∴2 = √(l/l-1.5)
=>4 = (l/l-1.5)
∴l = 4[l-1.5] = 4l – 6.0
∴4l – l = 6.0
3l = 6.0
l = 2.0m

You May Also Like