A simple pendulum, has a period of 5.77 seconds. When the pendulum is shortened by 3 m, the period is 4.60 seconds. Calculate the new length of the pendulum
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Correct Answer: Option A
Explanation:
Let the original length L=xm
;New length =( x -3 ) m
\(T_1\) = 5.77s; \(T_2\) = 4.60s,
\(T^2\) α L
⇒\(T^2\) = kL where K is constant
⇒ K = \(\frac{T^2_1}{L_1} = \frac{T^2_2}{L_2}\)
⇒\(\frac{5.77^2}{x}\) = \(\frac{4.60^2}{x-3}\)
⇒ \(\frac{33.29}{x}\) = \(\frac{4.60^2}{x-3}\)
⇒ 33.29(x-3) = 21.16x
⇒ 33.29x - 99.87 =21.16x
⇒12.13x = 99.87
;x =\(\frac{99.87}{12.13}\) = 8.23m
The new length of the pendulum
=x-3 = 8.23-3
=5.23m
Let the original length L=xm
;New length =( x -3 ) m
\(T_1\) = 5.77s; \(T_2\) = 4.60s,
\(T^2\) α L
⇒\(T^2\) = kL where K is constant
⇒ K = \(\frac{T^2_1}{L_1} = \frac{T^2_2}{L_2}\)
⇒\(\frac{5.77^2}{x}\) = \(\frac{4.60^2}{x-3}\)
⇒ \(\frac{33.29}{x}\) = \(\frac{4.60^2}{x-3}\)
⇒ 33.29(x-3) = 21.16x
⇒ 33.29x - 99.87 =21.16x
⇒12.13x = 99.87
;x =\(\frac{99.87}{12.13}\) = 8.23m
The new length of the pendulum
=x-3 = 8.23-3
=5.23m