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
5.23 m
6.42 m
4.87 m
7.26 m
Correct answer is A
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
New length of the pendulum
=x-3 = 8.23-3
=5.23m
