The length of two pendulum is 110 cm and 27.5 cm, calculate the ration of their time periods

T1 = 2π√27.5/√g

T1^2 = 4π^27.5g
T2 = 2π√27.5/√g
T2^2 = 4π^110g
T1^2/T2^2 = 4π^27.5g/4π^110g
T1^2/T2^2 = 27.5/110 = 275/1100 = 1/4
T1/T2 = √(1/4)
so T1: T2 = 1 : 2

To calculate the ratio of the time periods of the two pendulums, we can use the formula:

T = 2π√(L/g)

where T is the time period of the pendulum, L is the length of the pendulum, and g is the acceleration due to gravity (approximately 9.8 m/s²).

Let's calculate the time periods for each pendulum:

For the first pendulum with a length of 110 cm:
T₁ = 2π√(L₁/g)
T₁ = 2π√(110/100 * 9.8)
T₁ = 2π√(1.1 * 9.8)
T₁ ≈ 2π√10.78
T₁ ≈ 2π√(10.78)
T₁ ≈ 2π * 3.28
T₁ ≈ 6.49 seconds (rounded to two decimal places)

For the second pendulum with a length of 27.5 cm:
T₂ = 2π√(L₂/g)
T₂ = 2π√(27.5/100 * 9.8)
T₂ = 2π√(0.275 * 9.8)
T₂ ≈ 2π√2.6875
T₂ ≈ 2π√(2.6875)
T₂ ≈ 2π * 1.64
T₂ ≈ 10.28 seconds (rounded to two decimal places)

Now, we can calculate the ratio of their time periods:
Ratio = T₁ / T₂
Ratio = 6.49 / 10.28
Ratio ≈ 0.63 (rounded to two decimal places)

Therefore, the ratio of the time periods of the two pendulums is approximately 0.63.

To calculate the ratio of the time periods of two pendulums, we can use the formula for the time period of a simple pendulum:

T = 2π√(L/g),

where T is the time period, L is the length of the pendulum, and g is the acceleration due to gravity.

In this case, we have two pendulums with lengths L1 = 110 cm and L2 = 27.5 cm.

We can calculate the time period of the first pendulum using the formula:

T1 = 2π√(L1/g).

Similarly, we can calculate the time period of the second pendulum using the formula:

T2 = 2π√(L2/g).

To find the ratio of their time periods, we divide T1 by T2:

Ratio = T1 / T2.

To calculate the values, we need to know the value of acceleration due to gravity (g). Assuming it is approximately 9.8 m/s², we convert the lengths to meters and substitute the values into the formula:

For the first pendulum:
L1 = 110 cm = 1.1 m
T1 = 2π√(1.1 / 9.8) ≈ 0.668 seconds (rounded to three decimal places)

For the second pendulum:
L2 = 27.5 cm = 0.275 m
T2 = 2π√(0.275 / 9.8) ≈ 0.426 seconds (rounded to three decimal places)

Now we can calculate the ratio of their time periods:
Ratio = T1 / T2 ≈ 0.668 / 0.426 ≈ 1.568 (rounded to three decimal places)

Therefore, the ratio of the time periods of the two pendulums is approximately 1.568.

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