What should be the length of steel and copper rods at `0^(@)C` that the length of steel rod is 5 cm longer than copper at all termperature? Given `alpha_(Cu) = 1.7 xx 10^(5) .^(@)C^(-1)` and `alpha_(steel) = 1.1 xx 10^(5) .^(@)C^(-1)`.

What must be the lengths of steel and copper rods at 0^(@)C for the difference in their lengths to be 10 cm at any common temperature? (alpha_(steel)=1.2xx10^(-5).^(@)K^(-1)and alpha_("copper")=1.8xx10^(-5).^(@)K^(-1))

The length of the steel rod which would have the same difference in length with a copper rod of length 24cm at all temperatures. (alpha_("copper") = 18 xx 10^(-6) K^(-1) alpha_("steel") = 12 xx 10^(-6) k^(-1)) is -

Two fines steel wires , fastened between the projectors of a heavy brass bar, are just taut when the whole system is at 0^(@)C . What is the tensile stress in the steel wires the temperature of the system is raised by 200^(@)C ? ( alpha_("glass") = 2 xx 10^(-5) ^(@)C ^(-1), alpha_("steel") = 1.2 xx 10^(-5)"^(@)C^(-1), Y_("steel") = 200GNm^(-2) )

In a certain arrangement, two cylinders of brass and steel are laid side by side and there is a constant difference of length between them at any temperature. Calculate the lengths of these cylinders at 0^@C if there is a difference of 5 cm between their lengths at all temperatures. alpha_("brass") = 0.0000019^@C^(-1) alpha_("steel") = 1.2 xx 10^(-6) C^(-1)

A fine steel wire of length 4 m is fixed rigidly in a heavy brass frame as ashown in figure . It is just taut at 20^(@)C . The tensile stress developed in steel wire it whole system is heated to 120^(@)C is :- ( Given alpha _("brass") = 1.8 xx 10^(-5) .^(@)C^(-1), alpha_("steel") = 1.2 xx 10^(-5) .^(@)C, Y_("steel") = 2 xx 10^(11) Nm^(-2), Y_("brass")= 1.7xx10^(7) Nm^(-2) )

The design of some physical instrument requires that there be a constant difference in length of 10 cm between an iron rod and a copper cylinder laid side by side at all temperature find their lengths (alpha_(Fe)=11 xx 10^(6).^(@)C^(-1),alpha_(Cu)=17 xx 10^(-6) .^(@)C^(-1))

A heavy brass bar has projections at its ends as shown in the figure. Two find steel wires, fastened between the projections, are just taut (zero tension) when the whole systeam is at 0^(0)C . What is the tensile stress in the steel wires when the temperature of the systeam is raised to 300^(0)C ? Given that alpha_("brass") = 20 xx 10^(-6 ^(@))C^(-1) alpha_("steel") = 12 xx 10^(-6@)C^(-1) Y_("steel") = 2 xx 10^(11) Nm^(-2)

The coefficient of linear expansion 'alpha ' of a rod of length 2 m varies with the distance x from the end of the rod as alpha = alpha_(0) + alpha_(1) "x" where alpha_(0) = 1.76 xx 10^(-5) "^(@)C^(-1)"and" alpha_(1) = 1.2 xx 10^(-6)m^(-1) "^(@)C^(-1) . The increase in the length of the rod. When heated through 100^(@)C is :-