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A piece of metal weighs 46 g in air and ...

A piece of metal weighs 46 g in air and 30 g in lipuid of density `1.24 xx 10^3 kg m^(-3)` kept at `27^0C`. When the temperature of the liquid is raised to `42^0C` the metal piece weights 30.5 g . The density of the liqued at `42^0 C` is `1.20 xx 10^3 kg m^(-3)`. Calculate the coefficient of linear expandsion of the metal.

A

`1.15 xx 10^(-5) //""^(@) C `

B

`2.31 xx 10^(-5) //^(@) C `

C

`3.46 xx 10^(-5) //^@ C `

D

`0.96 xx 10^(-5) //^@ C`

Text Solution

Verified by Experts

The correct Answer is:
B
`W_0 = mg = 46 g wt . Theta_1 = 27 ^@ C `
`W_1 = 30 g = W_0 =B_1 implies B_1 = ( 46-30 ) g `
` implies B_1 = 16 g . Wt = V_1 rho_1 g`
`implies B_1 = 16 g- wt = V_1 rho_1 g `
`theta_2 = 42 ^@ C `
` W_2 = 30.5 g W_0 - B_2 implies B_2 = 15.5 g =V_2 rho_2 g `
` therefore (B_2)/(B_1) = (V_2 rho_2)/(V_1 rho_1 ) (15.5 )/( 16) = (1 + 3alpha _s xx 15 ) xx (1.2 )/( 1.24)`
` therefore alpha_S =2.31 xx 10^(-5) //^@ C`
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