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Q.

A uniform wire is cut into 10 segments of increasing length. Each segment is having a resistance of 8 $Ω$ more than that of previous segment. If the resistance of shortest segment is R and largest segment is 2 R. The original resistance of wire in ohm.

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a

1080

b

72

c

720

d

144

answer is D.

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Detailed Solution

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$R + 9 \times 8 = 2 R; R + 72 = 2 R \Rightarrow R = 72$
Common difference = 8
Sum of 'N' numbers $= \frac{N}{2} [2 a + (n - 1) d]$
$= 5 [2 \times 72 + (10 - 1) 8] = 1080$

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A uniform wire is cut into 10 segments of increasing length. Each segment is having a resistance of 8 Ω more than that of previous segment. If the resistance of shortest segment is R and largest segment is 2 R. The original resistance of wire in ohm.