A metal scale is graduated at `0^@C` . What would be the true length of an object which when measured with this scale at `25^@C`, reads 50 cm? `alpha` for metal = `18 xx 10^(-6)//^@C` .

Define co-efficient of linear and cubical expansion and establish a relation between them . The length of a copper wire is measured 40 cm by a metal scale when both are at the temperature of 25^@C . What would be the length of wire measured by the same scale when both are at 55^@C ? (alpha "for metal" = 1.1 xx 10^(-7) @C^(-1) and alpha for copper = 1.7 xx 10^(-7)@c^(-1))

A steel rod when measured with a zinc scale (alpha = 26 xx 10^(-6)//^@C) appears to be 1 m long when both rods are at 20^@C . If the zinc scale was graduated at 0^@C , what is the true length of the steel rod at 0^@C ? alpha for steel = 12 xx 10^(-6)//^@C .

A brass scale is correct at 20^@C . The length of a rod measured by it at 35^@C is 60 cm . What is the correct length of rod at that temperature ? ( alpha of brass = 18.9 xx 10^(-6) per^@C) .

A steel tyre is 1 m in diameter at 10^@C . To what temperature it must be raised so that it may just slip on a wheel 1.005 m in diameter ? alpha for steel = 12 xx 10^(-6)//^@C .

A metal sphere 10.01 cm in diameter is placed on a brass ring of internal diameter 10 cm at the same temperature of 12^@C . Find the temperature to which they should be heated together so that the metal sphere just passes through the ring . alpha_"metal" = 12 xx 10^(-6)//^@C and alpha_"brass" = 18 xx 10^(-6)//^@C

A clock with a copper pendulum beats seconds at 25^@C . Find the loss or gain perday when the temperature falls to 10^@C . Take co-efficient of linear expansion of copper = 18 xx 10^(-6)//^@ C

An iron plate has a circular hole of diameter 10 cm . Find the diameter of the hole when the plate is uniformly heated from 10^@C to 90^@C (alpha = 12 xx 10^(-6)//^@C) .

What should be the length of steel abd copper rods at 0^@C so that the difference in their lengths is 5.0 cm at all temperatures. Coefficient of linear expansion of copper is 1.7 xx 10^(-5) //^@ C and that of steel is 1.1 xx 10^(-5) //^@ C .

If a cylinder of diameter of 1 cm at 30^@C is fitted into a hole of diameter 0.9997 cm in a steel plate, find the temperature the fitting has to be done ? Co.eff.of linear expansion of steal is 12 xx 10^(-6)//^@ C