Question

A metal rod has a length of 1m at 30°C.
'a' of metal is 2.5x10-1°C. The temperature
at which it will be shortened by Imm is​

Answer 1

A metal rod has a length of 1m at 30°C .

coefficient of linear expansion, a = 2.5 × 10^-1 /°C.

we have to find temperature at which , it will be shortened by 1mm or 10^-3 m.

using formula, $l=l_0[1+a(T-T_0)]$

or, $l=l_0+l_0a(T-T_0)$

or, $\Delta l=l_0a(T-T_0)$

where, $l_0=1m,\Delta l=10^{-3}m$, $T_0$ = 30° and a = 2.5 × 10^-1 /°C

so, 10^-3 = 1 × 2.5 × 10^-1 (T - 30)

or, 10^-2 = 2.5(T - 30)

or, 10^-2/2.5 = T - 30

or, T = 30 + 0.01/2.5

or, T = 30 + 0.004 = 30.004°C

hence, answer should be 30.004°C