Question

The ratio of lengths of two simple pendulums is 1:9. The ratio of their time periods is​

Answer 1

Answer:

let length of first pendulum and second pendulum be L1 and L2

and time period be T1 andT1

Explanation:

Given : L1 : L2 = 1 :9

as we know,

T = 2π√L/g

T1 / T2 = √L1 / L2

= √1/9

=1/3

T1 : T2 = 1 / 3

Answer 2

Concept:

The time period is how long it takes for a wave to pass a location after going through one full cycle. The time period of a simple pendulum can be calculated by the formula, T = 2π√L/g.

Given:

The ratio of the length of two simple pendulums = 1:9

Find:

We need to determine the ratio of the two simple pendulum time periods.

Solution:

The formula to calculate time period is, T = 2π√L/g where T = time period, L = length of the pendulum and g = acceleration due to gravity

Since, the ratio of two simple pendulums is given as, L₁: L₂ = 1:9

Therefore, the above time period formula for one pendulum becomes, T₁ = 2π√L₁/g and for the second pendulum becomes, T₂ = 2π√L₂/g

Therefore, the ratio becomes, T₂/T₁  = √L₂/L₁ = √9/1 = 3

Therefore T₁ : T₂ = 1:3

Thus, the ratio of the time period of two pendulums is 1:3.

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