A meter scale made of steel , reads accirately at `25 ^(@) C ` Suppose in an experiment an accuracy of 0.06 mm in 1 m is required , the range of temperature in which the experiment can be performed with this meter scale is ( Coefficient of linear expansion of steel is `11xx10 ^(-6) // ""^(@) C `)

Options

A. `19^@C to 31^@C`
B. `25^@C to 32^@C`
C. `18^@C to 25^@C`
D. `18^@C to 32^@C`

Answer

A

Explanation

Answer(1) Co.efficient of linear expansion of steel, `alpha = 11 xx 10^-6/^@C`
Length, l = 1m .
Change in length, `Delta l = 0.06mm = 6 xx 10^-5m` .
`Delta l = l alpha Delta t` .
`Rightarrow Delta t = (Deltal)/(l.alpha) = (6 xx 10^-5)/(1 xx 11 xx 10^-6) = 5.45^@C`.
`therefore` Range of temperature = (25 - 5.45 to 25 + 5.45) = (19.55^@C to 30.45^@C`).
`approx 19^@C to 31^@C`.