A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is `(alpha cu=1.7xx10^(-5) K^(-1) " and " alpha Al=2.2xx10^(-5) K^(-1))`

Options

A. 68 cm
B. 6.8 cm
C. 113.9 cm
D. 88 cm

Answer

A

Explanation

`l._(Cu) = I_(Cu)(1 + alpha_(Cu) Delta T)....... (i)`
`l._(Al) = l_(Al) (1 + alpha_(Al) Delta T)`
By equation (ii)- (i)
`l._(Al) - l._(cu) = l_(Al) alpha_(Al) Delta T - (l_(Cu) + I_(Cu) alpha_(Cu) Delta T)`
`l._(Al) - l._(cu) = l_(Al) - I_(Cu) + (I_(Al) alpha_(Al) - I_(Cu) alpha_(Cu)) Delta T`
When increases in length is not depend on temperature
`alpha_(cu) l_(Cu) = alpha_Al l_(Al)`
`1.7 xx 10^(-5) xx 88 = 2.2 xx 10^(-5) xx I_(Al)`
`I_(Al) = 68 cm`.