Question

On heating a uniform metallic cylinder length increases by 3%. The area of cross-section of its base will increase by
(1) 1.5%
(2) 3%
(3) 9%
(4) 6%

Answer 1

On heating a uniform metallic cylinder length increases by 3%. The area of cross-section of its base will increase by 6%



α/β=1/2 β=2α β=2*3=6

Answer 2

Hey dear,

◆ Answer -
(4) ∆A/A = 6 %

◆ Explanation-
# Given-
∆l / l = 3 %
∆A / A = ?

# Solution-
Here, same stress will be applied for both linear as well as areal expansion.
i.e. F/A = same

Coefficient of linear expansion -
α = (F/A) / (∆l/l)

Coefficient of areal expansion -
β = (F/A) / (∆A/A)

There's a relationship,
β = 2 α

Putting values of α & β,
(F/A) / (∆A/A) = 2 (F/A) / (∆l/l)
∆A/A = 2 ∆l/l
∆A/A = 2 × 3%
∆A/A = 6 %

Therefore, Increase in area of cross section is 6 % .

Hope this helps you..