A thin brass sheet at 10° C, and a thin steel sheet at 20° C have the same surface area. The common temperature at which both would have the same area is (Coefficient of linear expansion for brass and steel are 19 × 10-60 C -1 and 11 × 10-6 ° C -1 respectively)

Question

A thin brass sheet at 10° C, and a thin steel sheet at 20° C have the same surface area. The common temperature at which both would have the same area is (Coefficient of linear expansion for brass and steel are 19 × 10-60 C -1 and 11 × 10-6 ° C -1 respectively) (A) -3.75° C (B) -2.75° C (C) +2.75° C (D) +3.75° C

Tardigrade Admin · Accepted Answer

The area of brass sheet at 10° C =l1 b1 The area of steel sheet at 20° C =l2 b2 Given that l1 b1=l2 b2 Let at temperature T° C the areas of brass and steel sheets be same. Length of brass sheet at T° C =l1[1+αb Δ Tb] Length of steel sheet at T° C =l2[1+αs Δ Ts] Breadth of brass sheet at T° C =b1[1+αb Δ Tb] Breadth of steel sheet at T° C =b2[1+αs Δ Ts] According to problem, l1[1+αb Δ Tb] × b1[1+αb Δ Tb] =l2[1+αs Δ Ts] × b2[1+αs Δ Ts] or l1 b1[1+αb Δ Tb]2=l2 b2[1+αs Δ Ts]2 or l1 b1[1+19 × 10-6 ×(10-T)]2=l2 b2[1+11 × 10-6(20-T)]2 or 19 × 10-6(10-T)=11 × 10-6(20-T) ∴ T=-(30/8)=-3.75° C

$- 3.7 5^{\circ} C$

$- 2.7 5^{\circ} C$

$+ 2.7 5^{\circ} C$

$+ 3.7 5^{\circ} C$

Q. A thin brass sheet at 10∘C, and a thin steel sheet at 20∘C have the same surface area. The common temperature at which both would have the same area is (Coefficient of linear expansion for brass and steel are 19×10−60C−1 and 11×10−6∘C−1 respectively)

−3.75∘C

−2.75∘C

+2.75∘C

+3.75∘C

$- 3.7 5^{\circ} C$

$- 2.7 5^{\circ} C$

$+ 2.7 5^{\circ} C$

$+ 3.7 5^{\circ} C$