1
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Question

# Two wires made of same material have their length are in the ratio 1:2 and their masses in the ratio 3:16. The ratio of resistance of two wires is.

A
34
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B
1:2
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C
2:1
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D
4:3
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Solution

## The correct option is D 4:3Given: ℓ1ℓ2=12,m1m2=316Step 1: Defining Resistance R=ρℓA ............(1) Density, d=mV=mAl ∴ A=mdℓPut the value of A in eq. (1), we get R=ρℓ2dm ..............(2)Step 2: Ratio of resistance of two wiresAs the two wires are made of the same material, so they will have the same density. Let R1 & R2 be the resistances of the two wires, so using equation (2), we get: R1=ρ ℓ21dm1 & R2=ρ ℓ22dm2 Dividing R1 & R2, we get: R1R2=(ℓ1ℓ2)2×(m2m1) ⇒ R1R2=(12)2×(163)=43 ∴ R1:R2=4:3 Hence, Option(D) is correct.

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