Question

if the length of a simple pendulam is made one-fourth then it's time period becomes .one fourth .four times double .half

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Answer 1

Answer :

We have to find change in time period of simple pendulum if it's length is made one-fourth$.$

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◈ Time period of simple pendulum in terms of length and acceleration due to gravity is given by

• T = 2π × √(L/g)

T denotes time period

l denotes length

g denotes acceleration due to gravity

ATQ, g remains constant so we can say that time period of simple pendulum is directly proportional to the sqrt of its length.

• T ∝ √L

➝ T₁ / T₂ = √L₁ / √L₂

➝ T₁ / T₂ = √L₁ / √(L₁ / 4)

➝ T₁ / T₂ = √4

➝ T₂ = T₁ / √4

➝ T₂ = T₁ / 2

Hence, time period of simple pendulum becomes half.