Question

Two pendulums begin to swing simultaneously. The first pendulum makes 9 full oscillations when the other makes 7. The ratio of lengths of the two pendulum is:

Answer 1

Let time period be t1 and t2 respectively and then,

》n1×t1=n2×t2

》n1/n2=t2/t1

》since t=2pi(L/g)^1/2 take l1 and l2 as different length in t1 and t2

now (n1/n2)^2=l2/l1 on solving

Thus on putting values l1/l2=49/81.

Answer 2

Given:

Oscillations made by first Pendulum = 9

Oscillations made by first Pendulum = 7

To Find:

The ratio of lengths of the two pendulum

Solution:

Let the time period of 1st pendulum be = T1

​ Le the time period of 2nd pendulum be = T 2

Similarly,

Let the length of 1st pendulum be = I1

​ Le the length of 2nd pendulum be = I 2

Now,

T1 ∝ √I1 and T2 ∝ √I2

Now,

T1/T2 = 7/9

√I1/√I2 = 7/9

I1/I2 = ( 7/9)²

I1/I2 = 49/81

Answer: The ratio of lengths of the two pendulums is 49/81

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