Question

The time period of two simple pendulums A and B are 4 s and 12 s respectively. What will be the ratio of their effective length ?​

Answer 1

Explanation:

Answer

T=2π

g

l

Time period does not depend on the weight of the bob.

So, the ratio of time period will be equal to 1.

Answer 2

Answer:

1 : 9 is the ratio of their effective length.

Explanation:

We have,

=> A's time period = 4 s

=> B's time period = 12 s

To find,

=> Ratio of their effective length.

Solution,

Ratio of A and B's time period :

>> A : B = 4 : 12 = 1 : 3

Relationship between effective length, time period of simple pendulum:

>> T=2π√(l/g)

For both the simple pendulums (time period) :

>> T1 = 2π√(l1/g)

>> T2 = 2π√(l2/g)

Dividing the both simple pendulums time period:

>> T1 = 2π√(l1/g)/T2 =2π√(l1/g)

>> 2π√(l1/g)/2π√(l2/g)

>> T1/T2 = √l1/√l2

Squaring on both sides:

=> l1/l2 = 1²/3²

=> l1/l2 = 1/9

∴ l1 : l2 = 1 : 9