The time period of two pendulums are 1.44s and 0.36s respectively. Calculate the ratio of their lengths.
A school SUBJECT is what you study, not the name of your school.
To calculate the ratio of the lengths of two pendulums based on their time periods, we can use the equation for the period of a pendulum:
T = 2π√(L/g),
where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
Given the time periods T1 = 1.44s and T2 = 0.36s, we can set up the following equations:
T1 = 2π√(L1/g),
T2 = 2π√(L2/g).
To find the ratio of their lengths, we can divide the two equations:
T1/T2 = (2π√(L1/g))/(2π√(L2/g)).
The 2π term cancels out, so we're left with:
T1/T2 = √(L1/g)/√(L2/g).
To simplify this further, we can take the square of both sides:
(T1/T2)^2 = (L1/g)/(L2/g).
Now, we can simplify the right-hand side:
(T1/T2)^2 = L1/L2.
Finally, we can take the square root of both sides to find the ratio of the lengths:
√((T1/T2)^2) = √(L1/L2).
Therefore, the ratio of the lengths is given by:
L1/L2 = √((T1/T2)^2).
Substituting the given values, we have:
L1/L2 = √((1.44s/0.36s)^2).
L1/L2 = √(4^2) = √16 = 4.
Hence, the ratio of the lengths of the two pendulums is 4.