A 12 cm wire is given a shape of a right angled triangle A B C having sides 3 cm, 4 cm and 5 cm as shown in the figure. The resistance between two ends (A B, BC, CA) of the respective sides are measured one by one by a multi-meter. The resistances will be in the ratio

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9: 16: 25

27: 32: 35

21: 24: 25

3: 4: 5

answer is B.

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Detailed Solution

Let ρ and A be resistivity and area of cross-section of the wire respectively. The wire is bent in the form of right triangle as shown in adjacent figure. Resistance of side AB is R1=ρ3A Resistance of side BC is R2=ρ4A Resistance of side AC is R3=ρ5A ∴ The resistance between the ends A and B is RAB=R1R2+R3R1+R2+R3=3ρA4ρA+5ρA3ρA+4ρA+5ρA=2712ρA The resistance between the ends B and C is RBC=R2R1+R3R2+R1+R3=4ρA3ρA+5ρA4ρA+3ρA+5ρA=3212ρA The resistance between the ends A and C is RAC=R3R1+R2R3+R1+R2 =5ρA3ρA+4ρA5ρA+3ρA+4ρA=3512ρA ∴ RAB:RBC:RAC=2712:3212:3512=27:32:35

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