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Question

A man is swinging on a swing made of 2 ropes of equal length L and in direction perpendicular to the plane of paper. The time period of the small oscillations about the mean position is


A

2π3L2g

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B

πLg

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C

2πL2g

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D

2πL23g

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Solution

The correct option is A

2π3L2g


Step 1: Given

Length of ropes is L.

Effective length of the swing is Leffective, which is AB in the below diagram.

Acceleration due to gravity is g.

Time period of an oscillation is T.

The angle made by the swing is 60°, as it makes an equilateral triangle.

Step 2: Formula used

  1. T=2πLeffectiveg
  2. sinθ=PH

Step 3: Find the effective length AB of the swing:

sin60°=PH32=ABLAB=32L

Step 4: Substitute the values to find the time period

T=2πLeffectiveg=2π3L2g=2π3L2g=2π3L2g

Hence, option (A) is correct.


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