# 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 x 10-6,/sup> per 0C, the period of the pendulum will have percentage increase of (A) -2 x 10-3 (B) -1 x 10-3 (C) 2 x 10-3 (D) 1 x 10-3

The fractional increment in time with temperature change

$\frac{\Delta&space;t}{t}=\frac{1}{2}\alpha&space;\Delta&space;T$ — (1)

where,

Δt/t is fractional increment

α is coefficient of linear expansion

ΔT is change in temperature

ΔT = 100C

α = 2 x 10-6 per 0C

From equation (1)

Δt/t = (1/2) x 2 x 10-6 x (10)

We get,

Δt/t = 10-5

Percentage change of period

%(Δt/t) = (Δt/t) x 100

= 10-5 x 100

We get,

= 10-3

= 1 x 10-3

Therefore, the correct option is (D)

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