An iron rod of length 50 cm is joined at an end to aluminium rod of length 100 cm. All measurements refer to `20^(0) C` . Find the length of the composite system at `100^(o) C` and its average coefficient of linear expansion. The coefficient of linear expansion of iron and aluminium are `12 X 10^(-6 ) C^(-1)` and `24 X10^(-6 ) C ^(-1)` respectively.

Find the ratio of the lengths of an iron rod and an aluminum rod for which the difference in the lengths in independent of temperature. Coefficients of linear expansion of iron and aluminum are 12 xx10^(-6)C^(-1) and 23 xx 10^(-6)C^(-1) respectively.

An iron rod and a copper rod lie side by side. An the temperature is changed, the difference in the length of the rods remains constant at a value of 10 cm. Find the lengths at 0^o C . Coefficients of linear expansion of iron and copper are 1.1 xx 10^(-5) C^(-1) and 1.7 xx 10^(-5) C^(-1) respectively.

A aluminum can of cylindrical shape contains 500cm^3 of water. The area of the inner cross section of the can is 125cm^2 . All measurements refer to 10^@C . Find the rise in the water level if the temperature increases to 80^@C . The coefficient of linear expansion of aluminum =23 xx 10^(-6)C^(-1) and the average coefficient of volume expansion of water= 3.2xx10^(-4)C^(-1) respectively.

When a metallic bar is heated from 0^@ C to 100^@C , its length increases by 0.05 %, what is the co-efficient of linear expansion of the metal?

A glass window is to be fit in an aluminum frame. The temperature on the working day is 40^@C and the glass window measures exactly 20 cm xx 30 cm. What should be the size of the aluminum frame so that there is no stress on the glass in winter even if the temperature drops to 0^@C ? Coefficients of linear expansion for glass and aluminum are 9.0 xx 10^(-6)C^(-1) and 24xx10^(-6)C^(-1) respectively.

A concrete slab has a length of 10 m on a winter night when the temperature is 0^@C . Find the length of the slab on a summer day when the temperature is 35^@C . The coefficient of linear expansion of concrete is 1.0xx10^(-5) C^(-1) .

Two steel rods and an aluminum rod of equal length l_0 and equal cross section are joined rigidly at their ends as shown in the figure below. All the rods are in a state of zero tension at 0^@C . Find the length of the system when the temperature is raised to theta . Coefficient of linear expansion of aluminum and steel are alpha_a and alpha_s respectively. Young's modulus of aluminum is Y_a and of steel is Y_s .

The volume of a glass vessel is 1000 cc at 20^@C . What volume of mercury should be poured into it at this temperature so that the volume of the remaining space does not change with temperature? Coefficients of cubical expansion of mercury and glass are 1.8 xx 10^(-4)C^(-1) and 9.0xx10^(-6)C^(-1). respectively.

The coefficient of x^(28) in the expansion of (1+x^3-x^6)^(30) is 1 b. 0 c. 30 C_6 d. ^30 C_3