Two brass rods A and B have lengths l and 2l | vedclass

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(C) The change in volume is given by the formula $\Delta V = \gamma V \Delta T$,where $V = \pi r^2 l$.Since both rods are made of the same material (b

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$2 : 1$

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(C) The change in volume is given by the formula $\Delta V = \gamma V \Delta T$,where $V = \pi r^2 l$.Since both rods are made of the same material (brass),the coefficient of volume expansion $\gamma$ is the same for both.For rod $A$: $V_A = \pi (2r)^2 l = 4\pi r^2 l$.For rod $B$: $V_B = \pi (r)^2 (2l) = 2\pi r^2 l$.Since the change in temperature $\Delta T$ is the same for both,the ratio of the increase in volume is:$\frac{\Delta V_A}{\Delta V_B} = \frac{\gamma V_A \Delta T}{\gamma V_B \Delta T} = \frac{V_A}{V_B} = \frac{4\pi r^2 l}{2\pi r^2 l} = \frac{2}{1}$.Therefore,the ratio is $2 : 1$.

Two brass rods $A$ and $B$ have lengths $l$ and $2l$ and radii $2r$ and $r$ respectively. If both are heated to the same temperature,the ratio of the increase in their volumes is:

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