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A child swings sitting and standinginside swing as shown in figure, thenperiod of oscillations has the relation(a) (๐‘‡)๐‘†๐‘–๐‘ก๐‘ก๐‘–๐‘›๐‘” = (๐‘‡)๐‘†๐‘ก๐‘Ž๐‘›๐‘‘๐‘–๐‘›๐‘”(b) (๐‘‡)๐‘†๐‘–๐‘ก๐‘ก๐‘–๐‘›๐‘” > (๐‘‡)๐‘†๐‘ก๐‘Ž๐‘›๐‘‘๐‘–๐‘›๐‘”(c) (๐‘‡)๐‘†๐‘–๐‘ก๐‘ก๐‘–๐‘›๐‘” < (๐‘‡)๐‘†๐‘ก๐‘Ž๐‘›๐‘‘๐‘–๐‘›๐‘”(d) 2(๐‘‡)๐‘†๐‘–๐‘ก๐‘ก๐‘–๐‘›๐‘” = (๐‘‡)๐‘†๐‘ก๐‘Ž๐‘›๐‘‘๐‘–๐‘›๐‘”

Question

A child swings sitting and standinginside swing as shown in figure, thenperiod of oscillations has the relation(a) (๐‘‡)๐‘†๐‘–๐‘ก๐‘ก๐‘–๐‘›๐‘” = (๐‘‡)๐‘†๐‘ก๐‘Ž๐‘›๐‘‘๐‘–๐‘›๐‘”(b) (๐‘‡)๐‘†๐‘–๐‘ก๐‘ก๐‘–๐‘›๐‘” > (๐‘‡)๐‘†๐‘ก๐‘Ž๐‘›๐‘‘๐‘–๐‘›๐‘”(c) (๐‘‡)๐‘†๐‘–๐‘ก๐‘ก๐‘–๐‘›๐‘” < (๐‘‡)๐‘†๐‘ก๐‘Ž๐‘›๐‘‘๐‘–๐‘›๐‘”(d) 2(๐‘‡)๐‘†๐‘–๐‘ก๐‘ก๐‘–๐‘›๐‘” = (๐‘‡)๐‘†๐‘ก๐‘Ž๐‘›๐‘‘๐‘–๐‘›๐‘”

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Solution

The period of oscillation of a pendulum (in this case, a swing) is determined by the length of the pendulum and the acceleration due to gravity. The mass of the pendulum and the position of the mass (whether the child is sitting or standing) does not affect the period of oscillation. Therefore, the period of oscillation when the child is sitting is equal to the period of oscillation when the child is standing. So, the correct answer is (a) (๐‘‡)๐‘†๐‘–๐‘ก๐‘ก๐‘–๐‘›๐‘” = (๐‘‡)๐‘†๐‘ก๐‘Ž๐‘›๐‘‘๐‘–๐‘›๐‘”.

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