The time period of a simple pendulum made using a thin copper wire of

The time period of a simple pendulum made using a thin copper wire of length L is T. Suppose the temperature of the room in which this simple pendulum is placed increases by 30°C, what will be the effect on the time period of the pendulum ?

[amp_mcq option1=”T will increase slightly” option2=”T will remain the same” option3=”T will decrease slightly” option4=”T will become more than 2 times” correct=”option1″]

This question was previously asked in

UPSC NDA-1 – 2017

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The time period of the pendulum, T, will increase slightly.

The time period (T) of a simple pendulum is given by the formula T = 2π * sqrt(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. The length of the pendulum is the length of the wire. Materials expand when heated due to thermal expansion.

When the temperature of the room increases, the copper wire of the simple pendulum will undergo thermal expansion, causing its length L to increase. According to the formula T = 2π * sqrt(L/g), the time period T is directly proportional to the square root of the length L (T ∝ √L). Since the length L increases with the increase in temperature, the time period T will also increase. The thermal expansion for a 30°C temperature change is typically small for common materials like copper, leading to a slight increase in the length and consequently a slight increase in the time period.

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