The change in volume (in cm 3 ) of a metal sphere of radius 10 cm , when its temperature is increased from 10° C to 60° C is (Given that coefficient of volume expansion of the sphere is .6.9 × 10-5 ° C -1)

Question

The change in volume (in cm 3 ) of a metal sphere of radius 10 cm , when its temperature is increased from 10° C to 60° C is (Given that coefficient of volume expansion of the sphere is .6.9 × 10-5 ° C -1) (A) 2.3 π (B) 4.6 π (C) 6.9 π (D) 9.2 π

Tardigrade Admin · Accepted Answer

(Δ V / V )=&gamma; Δ T Δ V =&gamma; V Δ T =6.9 × 10-5 × (4/3) π × 1000 × 50 =4.6 π

Q. The change in volume (in $c m^{3}$ ) of a metal sphere of radius $10 c m,$ when its temperature is increased from $1 0^{\circ} C$ to $6 0^{\circ} C$ is (Given that coefficient of volume expansion of the sphere is $6.9 \times 1 0^{- 5}^{\circ} C^{- 1})$

$2.3 π$

$4.6 π$

$6.9 π$

$9.2 π$

$\frac{Δ V}{V} = γ Δ T$
$Δ V = γV Δ T$
$= 6.9 \times 1 0^{- 5} \times \frac{4}{3} π \times 1000 \times 50$
$= 4.6 π$

Q. The change in volume (in cm3 ) of a metal sphere of radius 10cm, when its temperature is increased from 10∘C to 60∘C is (Given that coefficient of volume expansion of the sphere is 6.9×10−5∘C−1)

2.3π

4.6π

6.9π

9.2π