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Masses of the three wires of same material are in the ratio of  1 : 2 : 3 and their lengths in the ratio of 3 : 2 : 1. Electrical resistance of these wires will be in the ratio of:

Option: 1

1:1:1


Option: 2

1:2:3


Option: 3

9:4:1


Option: 4

27:6:1


Answers (1)

best_answer

Mass, \mathrm{M}=$ volume $\times$ density $=\mathrm{A} l \times \mathrm{d} \quad$ or $\quad \mathrm{A}=\mathrm{M} / l \mathrm{~d}

Resistance, \mathrm{R}=\rho l / \mathrm{A}=\rho l /(\mathrm{M} / l \mathrm{~d})=\frac{\rho l^2 \mathrm{~d}}{\mathrm{M}}

So, \mathrm{R} \propto l^2 / \mathrm{M}

Thus, \mathrm{R}_1: \mathrm{R}_2: \mathrm{R}_3=\frac{l_1^2}{\mathrm{M}_1}: \frac{l_2^2}{\mathrm{M}_2}: \frac{l_3^2}{\mathrm{M}_3}=\frac{3^2}{1}: \frac{2^2}{2}: \frac{1^2}{3}=27: 6: 1

Hence option 4 is correct.

Posted by

Rishi

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