Two uniform brass rods A and B of length ' l ' and ' 2 l ' and their radii ' 2 r ' and ' r ' respectively are heated to same temperature. The ratio of the increase in the volume of rod A to that of rod B is

Step-by-step solution

Let the original temperature be 0^ C Volume of A = V ₁=l (2 r )^2 After heating, volume of A will become aligned & V ₁^ = V ₁(1+ T ) & ( V ₁^ - V ₁ ) V ₁ = T V ₁^ - V ₁ V ₁ aligned Similarly for rod B, aligned & ( V ₂^ - V ₂ ) V ₂ = T V ₂^ - V ₂ V ₂ & V ₁ V ₂ = l(2 r )^2 2 l r ^2 = 2 1 aligned