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Q.

Two uniform brass rods A and B of lengths $l a n d 2 l$ and radii $2 r a n d r$ , respectively are heated to the same temperature. The ratio of the increase in the length of A to that of B is

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a

$2 : 1$

b

$1 : 2$

c

$1 : 1$

d

$1 : 4$

answer is B.

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Detailed Solution

The increase in length due to heating is independent of the radius of the rod. The increase in the length of rod A is
$Δ l = α l Δ t$
and of $rod B$ is
$Δ l^{'} = α l^{'} Δ t = 2 α l Δ t (∵ l^{'} = 2 l)$
$∴ \frac{Δ l}{Δ l^{'}} = \frac{1}{2}$

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