A simple pendulum, has a period of 5.77 seconds. When the...
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
T1 = 5.77s; T2 = 4.60s,
T2 α L
⇒T2)=kLwhereKisconstant⇒K=\(T21L1 = T22L2
⇒5.772x = 4.602x−3
⇒ 33.29x = 4.602x−3
⇒ 33.29(x-3) = 21.16x
⇒ 33.29x - 99.87 =21.16x
⇒12.13x = 99.87
;x =99.8712.13 = 8.23m
New length of the pendulum
=x-3 = 8.23-3
=5.23m