"the period of a pendulum, T (in seconds) varies directly with the square root of the length of the pendulum, L (in centimeters)". Given that a pendulum of length 9cm has a period of 0.63 seconds, find:

Question

a) The period of a pendulum of length 25cm

b) The length of a pendulum whose period is 1.5 seconds,

thanks :)

Answer 1

Given
T seconds =k √L (cm)

where k is an arbitrary constant to be determined.

Also given

0.63=k√9
Therefore we can determine the constant k.
k=0.63/√9=0.21

The relation now reads:
T(L)=0.21√L
where T is period in seconds
and L is length of pendulum in cm.

The problem reduces to:
a) T(25)=?
b) if T(L)=1.5 s, what is L?

Can you take it from here?

Answer 2

T = k√L
so, T/√L is constant.

(a) .63/√9 = T/√25

(b) .63/√9 = 1.5/√L