Show that the coefficient of area expansions, `(DeltaA//A)//DeltaT`, of a rectangular sheet of the solid is twice its linear expansively, `alpha_(l).(alpha_(l)=10^(-5)K^(-1))`

A large steel wheel is to be fitted on to a shaft of the same material. At 27 ^(@) C , the outer diameter of the shaft is 8.70 cm and the diameter of the central hole in the wheel is 8.69 cm. The shaft is cooled using dry Icel. At what temperature of the shaft does the wheel slip on the shaft? Assume coefficient of linear expansion of the steel to be constant over the required temperature range: alpha_("steel ") = 1.20 xx 10^(-5) K^(-1) .

A large steel wheel is to be fitted on to a shaft of the same material. At 27^(@)C , the outer diameter of the shaft is 0.70 cm and the diameter of the central hole in the wheel is 8.69 cm. The shaft is cooled using 'dry ice'. At what temperature of the shaft does the wheel slip on the shaft ? Assume coefficient of linear expansion of the steel to be constant over the required temperature range : alpha_("steel")=1.20xx10^(-5)K^(-1) .

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 :-

Obtain relation between coefficient of volume expansion (alpha_(V)) and coefficient of linear expansion (alpha_(l)) .

In a vernier callipers the main scale and the vernier scale are made up different materials. When the room temperature increases by DeltaT^(@)C , it is found the reading of the instrument remains the same. Earlier it was observed that the front edge of the wooden rod placed for measurement crossed the N^(th) main scale division and N + 2 MSD coincided with the 2nd VSD. Initially, 10 VSD coincided with 9MSD. If coefficient of linear expansion of the main scale is alpha_(1) and that of the vernier scale is alpha_(2) then what is the value of alpha_(1)//alpha_(2) ? (Ignore the expansion of the rod on heating)

Two rods each of length L_(2) and coefficient of linear expansion alpha_(2) each are connected freely to a third rod of length L_(1) and coefficient of expansion alpha_(1) to form an isoscles triangle. The arrangement is supported on a knife-edge at the midpoint of L_(1) which is horizontal. what relation must exist between L_(1) and L_(2) so that the apex of the isoscles triangle is to remain at a constant height from the knife edge as the temperature changes ?

A liquid with coefficient of volume expansion gamma is filled in a container of a material having coefficient of linear expansion alpha . If the liquid overflows on heating, then

A bimetallic strip of thickness d and length L is clamped at one end at temperature t_(1) . Find the radius of curvature of the strip if it consists of two different metals of expansivity alpha_(1) and alpha_(2) (alpha_(1) gt alpha_(2) ) when its temperature rises to t_(2) "^(@)C .

A copper rod of 88cm and an aluminimum rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is: (alpha_(Cu) =1.7 xx 10^(-5) K^(-1) and alpha_(Al)= 2.2 xx 10^(-5) K^(-1))

A rod has variable co-efficient of linear expansion alpha = (x)/(5000) . If length of the rod is 1 m . Determine increase in length of the rod in (cm) on increasing temperature of the rod by 100^(@)C .