A uniform metal rod is used as a bar pendulum. If the room temperature rises by 10 ° C , and the coefficient of linear expansion of the metal of the rod is 2× 10- 6 ° C- 1 , the period of the pendulum will have a percentage increase of

Question

A uniform metal rod is used as a bar pendulum. If the room temperature rises by 10 ° C , and the coefficient of linear expansion of the metal of the rod is 2× 10- 6 ° C- 1 , the period of the pendulum will have a percentage increase of (A) -2× 10- 3 (B) -1× 10- 3 (C) 2× 10- 3 (D) 1× 10- 3

Tardigrade Admin · Accepted Answer

The fractional change in period (Δ T/T)=(1/2)α Δ θ (Δ T/T)=(1/2)× 2× 10- 6× 10=10- 5 % change in time period = (Δ T/T)× 100=10- 5× 100=10- 3

Q. A uniform metal rod is used as a bar pendulum. If the room temperature rises by $10^{\circ} C$ , and the coefficient of linear expansion of the metal of the rod is $2 \times 1 0^{- 6}^{\circ} C^{- 1}$ , the period of the pendulum will have a percentage increase of

$- 2 \times 1 0^{- 3}$

$- 1 \times 1 0^{- 3}$

$2 \times 1 0^{- 3}$

$1 \times 1 0^{- 3}$

The fractional change in period
$\frac{Δ T}{T} = \frac{1}{2} α Δ θ$
$\frac{Δ T}{T} = \frac{1}{2} \times 2 \times 1 0^{- 6} \times 10 = 1 0^{- 5}$
% change in time period = $\frac{Δ T}{T} \times 100 = 1 0^{- 5} \times 100 = 1 0^{- 3}$

Q. A uniform metal rod is used as a bar pendulum. If the room temperature rises by 10∘C , and the coefficient of linear expansion of the metal of the rod is 2×10−6∘C−1 , the period of the pendulum will have a percentage increase of

−2×10−3

−1×10−3

2×10−3

1×10−3