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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 volume of A to that of B is

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a

1 : 1

b

1 : 2

c

2 : 1

d

1 : 4

answer is C.

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Detailed Solution

Let the original temperature be 0°C.Volume of A,V1=l×π(2r)2;V1'=V1(1+γΔT) V1'-V1V1=γΔT⇒V1'-V1∝V1Similarly, V2'-V2V2=γΔT⇒V2'-V2∝V2∵ ΔV1ΔV2=l(2r)22lr2=21

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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 volume of A to that of B is