Solved Numerical Problem No. 3 ( Unit-7: Oscillation); HSSC-1 (Class-11); Physics (New Book/KPK Text Board, Peshawar) With Verified Answers

Calculate the length of a second pendulum having a time period of 2s at a plate where g = 9.8 m s⁻². (L = 0.992 m) 

Given:

The time period of the second pendulum = T = 2 s

Value of acceleration due to gravity = g = 9.8 m s⁻²

To Find:

Length of second pendulum = L = ?

Solution:

The formula for the Time Period of the pendulum is 

T = 2π `\sqrt frac{L}{g}`

To separate the L from this formula we will take square on both sides and by simplifying we get

L = `\frac {T^2 g}{(2π)^2}`

by putting values

L = `\frac {(2s)^2 ｘ 9.8 m s⁻²}{(2 ｘ 3.1416)^2}`

 

L = `\frac {4 s² ｘ 9.8 m s⁻²}{(6.283185)^2}`

L = `\frac {39.2 m}{39.478}`

L = 0.9929 m ------------Ans.

Hence, the length L of the second pendulum at g = 9.8 m s⁻² is 0. 9929 m

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