The coefficient of volume expansion (β) is given as 49×10−5K−1. The formula to determine the change in volume due to thermal expansion is: ∆V=Vβ∆T Here: ∆V is the change in volume. V is the original volume. β is the coefficient of volume expansion. ∆T is the change in temperature. Given that the temperature change (∆T) is 50∘C, we have:
∆V=V⋅(49×10−5K−1)⋅50 ∆V=V⋅(49×10−5×50) ∆V=V⋅(2450×10−5) ∆V=V⋅0.0245 This indicates that the volume increases by 2.45%. Since density (ρ) is inversely proportional to volume ( V ), a 2.45% increase in volume will result in a 2.45% decrease in density. Thus, the percentage change in density is 2.45%. Hence, the correct option is: Option D: 2.45