Question

the time period of two pendulum are 2s and 1.2s .Find the ratio of the length

Answer 1

Explanation:

T1 : T2 = √l : √l2

L1 : L2 = T1² : T2²

= (T1/T2)² = (2/1.2)²

= (5/3)² = 25 : 9

Answer 2

Answer:

The ratio of the length of the pendulum is 25:9.

Explanation:

The pendulum's time period is given as,

$T=2\pi\sqrt{\frac{l}{g} }$       (1)

Where,

T=time period of the pendulum

l=length of the pendulum

g=acceleration due to gravity

We can also write equation (1) as;

$\frac{T_1}{T_2}=\sqrt{\frac{l_1}{l_2} }$

$\frac{l_1}{l_2}=\frac{T_1^2}{T_2^2}$        (2)

From the question we have,

$\frac{T_1}{T_2}=\frac{2}{1.2}$    (3)

Inserting equation (3) in equation (2) we get;

$\frac{l_1}{l_2}=(\frac{2}{1.2})^2$

$\frac{l_1}{l_2}=\frac{25}{9}$

The ratio of the length of the pendulum is 25:9.

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