A steel tyre is 100 cm in diameter at `25^@C`. To what temperature must it be heated so that it will just slip on a cartwheel 100.3 cm in diameter? (alpha_(steel)=1.2 xx 10^-5//^@C`)

A steel tyre of 1.2 m inner diameter at 20^@C is to be fitted on a cartwheel of 120.33 cm diameter of the tyre. Calculate the temperature to which the steel tyre is to be raised so that it will just slip on the wheel. (alpha_(Steel) = 11 xx 10^-6//^@C)

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

Railway tracks are laid with gaps for expansion. The gap between the steel rails 20 m long is 1.2 cm at 10^@C . The temperature at which the steel rails just touch each other is ( prop steel = 12 xx 10^-6//^@C)

A steel wire 2 mm in diameter is just stretched between two fixed points at a temperature of 20^(@)C. If the temperature falls to 10^(@)C, then the tension in the wire is (The coefficient of linear expansion of steel = 11xx10^(-6)//^(@)C and Y for steel 2.1 xx10^(11)N//m^(2))

The difference between the lengths of steel rod and a brass rod is 0.6 at all temperatures. What are their lengths at 0^@C ? (alpha_Steel = 12 xx 10^-6//^@C , (alpha_(brass)= 18 xx 10^-6//^@C )

A nylon rope of 2 cm in diameter has a breaking strength of 1.5 xx 10^(5) N . The breaking strength of a similar rope of 1cm in diameter is

An iron tyre is to be fitted onto a wooden wheel 1 m in diameter. The diameter of tyre is 6 mm smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of (the coefficient of cubical expansion of iron is 3.6 xx 10^-5/^@C)

Railway lines are laid with gaps to allow for expansion. If each line is 10 m long at 20^@C , what should be the length of the gap to be kept between two rails to allow for expansion if the maximum temperature that can be reached is 50^@C ? (alpha_(steel)=1.2 xx 10^-6//^@C)

Practice problems : Increase in the length of a steel rod is 0.06 cm . When its temperature is increased by 70 ⁰C . Find its initial length . [ codfficient of linear expansion of steel = 1.3 x 10^-5 (1/ ⁰C) ] .