Question

A pendulum A completes 25 oscillations in 30 seconds,and pendulum in 25 seconds. The ratio of the time periods of A and B is?

Answer 1

Step-by-step explanation:

your answer is ---

°•° A simple pendulum completes 10 oscillation in 25 second

So, it's time period is T1 = 10/25 sec

•°•

T1 = 2π√L1/g

=> T1^2 = 4π^2 ×L1/g

=>( 10/25 )^3= 4π^2×L1/g

=> (100/625×g)/4π^2 = L1

°•° another pendulum complete 11 oscillation in 25 second

So, it's time period is T2 = 11/25 second

•°•

T2 = 2π√L2/g

=> (11/25)^2 = 4π^2×L2^2/g

=> (121/625×g)/4π^2 = L2

•°•

L1/L2 = 100/121

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Answer 2

The ratio of the time periods of A and B=36:25

Step-by-step explanation:

Pendulum A completes number of oscillations in 30 seconds=25

Therefore, frequency of pendulum A,=$f_1=\frac{25}{30}=\frac{5}{6} Hz$

Time period of pendulum A=$T=\frac{1}{f_1}=\frac{6}{5}$ sec

Pendulum B completes number of oscillations in 25 second=30

Frequency of pendulum B=$f_2\frac{30}{25}=\frac{6}{5} Hz$

Time period of pendulum B=$T'=\frac{1}{f_2}=\frac{5}{6}$ sec

According to question

$\frac{T}{T'}=\frac{\frac{6}{5}}{\frac{5}{6}}=\frac{6}{5}\times \frac{6}{5}$

$\frac{T}{T'}=\frac{36}{25}$

$T:T'=36:25$

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