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Question

A uniform metal rod is used as a bar pendulum. If the room temperature rises by 100C, and the coefficient of linear expansion of the metal of the rod is 2×10-6perdegreeC, the period of the pendulum will have a percentage increase of


A

-2×10-3

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B

-1×10-3

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C

2×10-3

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D

1×10-3

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Solution

The correct option is D

1×10-3


Step 1: Given information

Coefficient of linear expansion, α=2×10-6perdegreeC

Change in temperature, ΔT=10°C

Step 2: Calculation

We know,

The fractional increment in time with temperature change:

tt=12αT

By substituting the values, we get

=12×2×10-6×10=10-5

The percentage change of period be:

%tt=tt×100=10-5×100=10-3=1×10-3

Therefore, option D is the correct choice.


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