The periodic time, t, of a pendulum range directly as the square root of its length, l. t = 6 when l = 9. If l = 25 then the periodic time, T exists at 10.
The period, or periodic time, of a periodic variation of a quantity, exists described as the time interval between two consecutive repetitions.
Given: The periodic time, t, of a pendulum goes directly as the square root of its length, l if t = 6 when l = 9.
If [tex]T \alpha\ l^2[/tex] then [tex]T^2[/tex] α [tex]\sqrt{l}[/tex]
[tex]T^2 = l[/tex]
Let, [tex]T^2 = kl,[/tex] where k exists constant
t = 6 when l = 9.
So, [tex]6^2 = k*9[/tex]
[tex]k = 6^2/9 = 4[/tex]
[tex]T^2 = 4*l[/tex]
If l = 25
[tex]T^2 = 4 * 25 = 100[/tex]
[tex]T = \sqrt{100}[/tex]
T = 10
Therefore, the periodic time, T exists 10.
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