A metal rod is used as a bar pendulum. If the room temperature rise by 10° C and coefficient of linear expansion of the metal of the rod is 3 × 10-5 per ° C , the period of pendulum will have percentage increases of

Question

A metal rod is used as a bar pendulum. If the room temperature rise by 10° C and coefficient of linear expansion of the metal of the rod is 3 × 10-5 per ° C , the period of pendulum will have percentage increases of (A) 0.816 % (B) 0.15 % (C) 0.01 % (D) 0.015 %

Tardigrade Admin · Accepted Answer

(Δ T / T )=(1/2) α Δ θ=(1/2) × 3 × 10-5 × 10=15 × 10-5 % increase =(Δ T / T ) × 100 =15 × 10-5 × 100 =15 × 10-3=0.015 %

Q. A metal rod is used as a bar pendulum. If the room temperature rise by $1 0^{\circ} C$ and coefficient of linear expansion of the metal of the rod is $3 \times 1 0^{- 5}$ per $^{\circ} C,$ the period of pendulum will have percentage increases of

$0.816%$

$0.15%$

$0.01%$

$0.015%$

$\frac{Δ T}{T} = \frac{1}{2} α Δ θ = \frac{1}{2} \times 3 \times 1 0^{- 5} \times 10 = 15 \times 1 0^{- 5}$
$%$ increase $= \frac{Δ T}{T} \times 100$
$= 15 \times 1 0^{- 5} \times 100$
$= 15 \times 1 0^{- 3} = 0.015%$

Q. A metal rod is used as a bar pendulum. If the room temperature rise by 10∘C and coefficient of linear expansion of the metal of the rod is 3×10−5 per ∘C, the period of pendulum will have percentage increases of

0.816%

0.15%

0.01%

0.015%