An aluminium measuring rod, which is correct at 5° C measures the length of a line as 80 cm at 45° C. If thermal coefficient of linear expansion of aluminium is 2.50 × 10-5 / ° C, the correct length of the line is:

Question

An aluminium measuring rod, which is correct at 5° C measures the length of a line as 80 cm at 45° C. If thermal coefficient of linear expansion of aluminium is 2.50 × 10-5 / ° C, the correct length of the line is: (A) 80.08 cm (B) 79.92 cm (C) 81.12 cm (D) 79.62 cm

Tardigrade Admin · Accepted Answer

The 80 cm mark on the aluminium rod is really at a greater distance from the zero position than indicated because of the increase in temperature Δ θ=40° C. The increased length is Δ L =αA l LA l Δ θ =(2.50 × 10-5)(80)(40)=0.08 cm The correct length of the line is L=80+0.08=80.08 cm

Q. An aluminium measuring rod, which is correct at $5^{\circ} C$ measures the length of a line as $80 c m$ at $4 5^{\circ} C$ . If thermal coefficient of linear expansion of aluminium is $2.50 \times$ $1 0^{- 5} /^{\circ} C$ , the correct length of the line is:

$80.08 c m$

$79.92 c m$

$81.12 c m$

$79.62 c m$

Q. An aluminium measuring rod, which is correct at 5∘C measures the length of a line as 80cm at 45∘C. If thermal coefficient of linear expansion of aluminium is 2.50× 10−5/∘C, the correct length of the line is:

80.08cm

79.92cm

81.12cm

79.62cm

The 80cm mark on the aluminium rod is really at a greater distance from the zero position than indicated because of the increase in temperature Δθ=40∘C. The increased length is ΔL=αAl​LAl​Δθ =(2.50×10−5)(80)(40)=0.08cm The correct length of the line is L=80+0.08=80.08cm

Q. An aluminium measuring rod, which is correct at $5^{\circ} C$ measures the length of a line as $80 c m$ at $4 5^{\circ} C$ . If thermal coefficient of linear expansion of aluminium is $2.50 \times$ $1 0^{- 5} /^{\circ} C$ , the correct length of the line is:

$80.08 c m$

$79.92 c m$

$81.12 c m$

$79.62 c m$