The volume of a metal sphere increases by 0.24 % when its temperature is raised by 40°C. The coefficient of linear expansion of the metal is

Question

The volume of a metal sphere increases by 0.24 % when its temperature is raised by 40°C. The coefficient of linear expansion of the metal is (A) 2 × 10-5 °C-1 (B) 6 × 10-5 °C-1 (C) 18 × 10-5 °C-1 (D) 1.2 × 10-5 °C-1

Tardigrade Admin · Accepted Answer

From, VT=V0(1+&gamma;Δ T) ⇒ (VT-V0/V0)=&gamma;Δ T (0.24/100)=&gamma; 40 °C &gamma;=(0.24/100 × 40)=6 × 10-5 °C-1 Coefficient of linear expansion, α=(&gamma;/3)=(6×10-5/3) =2 × 10-5 °C-1

Q. The volume of a metal sphere increases by $0.24%$ when its temperature is raised by $4 0^{\circ} C$ . The coefficient of linear expansion of the metal is

$2 \times 1 0^{- 5}^{\circ} C^{- 1}$

$6 \times 1 0^{- 5}^{\circ} C^{- 1}$

$18 \times 1 0^{- 5}^{\circ} C^{- 1}$

$1.2 \times 1 0^{- 5}^{\circ} C^{- 1}$

Q. The volume of a metal sphere increases by 0.24% when its temperature is raised by 40∘C. The coefficient of linear expansion of the metal is

2×10−5∘C−1

6×10−5∘C−1

18×10−5∘C−1

1.2×10−5∘C−1

From, VT​=V0​(1+γΔT) ⇒V0​VT​−V0​​=γΔT 1000.24​=γ40∘C γ=100×400.24​=6×10−5∘C−1 Coefficient of linear expansion, α=3γ​=36×10−5​ =2×10−5∘C−1

Q. The volume of a metal sphere increases by $0.24%$ when its temperature is raised by $4 0^{\circ} C$ . The coefficient of linear expansion of the metal is

$2 \times 1 0^{- 5}^{\circ} C^{- 1}$

$6 \times 1 0^{- 5}^{\circ} C^{- 1}$

$18 \times 1 0^{- 5}^{\circ} C^{- 1}$

$1.2 \times 1 0^{- 5}^{\circ} C^{- 1}$