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The massses of the three wires of copper...

The massses of the three wires of copper are in the ratio 1 : 3 : 5. And their lengths are in th ratio 5 : 3 : 1. the ratio of their electrical resistance is

A

`1:3:5`

B

`5:3:1`

C

`1:25:125`

D

`125:45:3`

Text Solution

Verified by Experts

The correct Answer is:
D
`R= (rhol)/(pi r^(2) )`. But `m = pir^(2) ld therefore pi r^(2) = (m) /( ld)`
`therefore R = ( rho l^(2) d)/(m) , R_(1) = ( rhol_(1)^(2) d)/( m_(1) ), R_2 = (rho l_(2)^(2) d)/(m_(2) ) , R_(3) = (rho l_(3)^(2) d)/( m_(3) )`
`R_1: R_2 :R_3 = (l_(1)^(2))/(m_1): (l_(2)^(2))/(m_2): (l_(3)^(2))/(m_(3))`
`R_1 : R_(2) : R_(3) = (25)/ (1): (9)/( 3) : (1)/(5) = 125 : 45 :3`
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