Answer: a)2.542cm
Explanation:
According to area expansivity which is defined as change in area per unit area for degree rise in kelvin.
Area expansivity= A2-A1/A1(¶2-¶1)
A2-A1 is change in area
¶2-¶1 is temperature change
A2 if final area
A1 is initial area
¶2 is final temp = 91°C
¶1 is initial temp= 26°C
coefficient of linear expansion for steel is 11 ✕ 10−6 (°C)−1.
Area of the spherical steel ball = Πd²/4
A1= Π×2.54²/4
A1 = 5.07cm²
Area expansivity = 2×linear expansion = 2×11 ✕ 10−6 (°C)−1.
= 22 ✕ 10−6 (°C)−1.
Substituting in the formula to get final area A2
22 ✕ 10−6 (°C)−1 = A2-5.07/5.07(91-26)
22 ✕ 10−6 (°C)−1 = A2-5.07/329.55
A2-5.07 = 0.0073
A2 = 0.0073+5.07
A2= 5.0073cm²
To get final diameter
A2=Πd²/4
5.0073=Πd²/4
20.309 = Πd²
d² = 20.309/Π
d²=6.46
d= √6.46
d= 2.542cm
