When a block of iron in mercury at `0^@C,` fraction `K_1`of its volume is submerged, while at the temperature `60^@C,` a fraction `K_2` is seen to be submerged. If the coefficient of volume expansion of iron is `gamma_(Fe)` and that of mercury is `gamma_(Hg),` then the ratio `(K_1)//(K_2)` can be expressed as

When a piece of metal floats in mercury at T^@C , a fraction f_1 of its volume is submerged. If their temperature is increased by Delta T ""^@C , fraction f_2 of metal piece is seen to be submerged. If the coefficients of volume expansion of the metal and the mercury are gamma_1 and gamma_2 , respectively, then the ratio f_1//f_2 is

The value of coefficient of volume expansion of glycerin is 5xx10^(4)K^(-1) . The fractional change in temperature is :

A wooden cylindrical block floats vertically with 70% of its volume immersed in a liquid at 0^@C . When temperature increases to 70^@C , the block sinks in the liquid. The coefficient of cubical expansion of liquid in K^(-1) is

An iron sphere of radius 10 cm is at temperature , 10^(@)C . If the sphere is heated upto temperature 110^(@)C , find the change in the volume of the sphere coefficient of linear expansion of iron = 11 xx 10^(-6) .^(@)C^(-1)

Determine the lengths of an iron rod and copper ruler at 0^@ C if the difference in their lengths at 50^@ C and 450^@ C is the same and is equal to 2 cm. the coefficient of linear expansion of iron =12xx10^(-6)//K and that of copper =17xx10^(-6)//K .

A glass bulb contains air and mercury. What fraction of the bulb must be occupied by mercury if the volume of air in the bulb is to remain constant at all temperatures? The coefficent of linear expansion of glass is 9xx10^(-6)//K .

At 4^(@)C, 0.98 of the volume of a body is immersed in water. The temperature at which the entire body gets immersed in water is (neglect the expansion of the body ) ( gamma_(w) = 3.3 xx10 ^(-4)K^(-1) ):-

A glass cylinder contains m_0=100g of mercury at a temperature of t_0=0^@C . When temperature becomes t_1=20^@C the cylinder contains m_1=99.7g of mercury The coefficient of volume expansion of mercury gamma_(He)=18xx(10^(-5)//^(@)C Assume that the temperature of the mercury is equal to that of the cylinder. The corfficient of linear expansion of glass alpha is

An iron sphere has a radius 8 cm at a temperature of 0^(@)C . Calculate the change in volume of the sphere if is temperature is raised to 80^(@)C . Coefficient of liner expansion of iron =11xx10^(-6) .^(@)C^(-1) .

Solids and liquids both expands on heating. The density of substance decreases on expanding according to the relation rho_(2) = (rho_(1))/(1 + gamma(T_(2)- T_(1))) , where , rho_(1) rarr "density at" T_(1) , rho_(2) rarr "density at" T_(2) , gamma rarr coefficient of volume expansion of substances. When a solid is submerged in a liquid , liquid exerts an upward force on solid which is equal to the weight of liquid displaced by submerged part of solid. Solid will float or sink depends on relative densities of solid and liquid . A cubical block of solid floats in a liquid with half ot its volume submerged in liquid as shown in figure (at temperature T ) alpha_(S) rarr Coefficient of linear expansion of solid gamma_(L) rarr "Coefficient of volume expansion of liquid" rho_(S) rarr "Density of solid at temperature" T rho_(L) rarr" Density of liquid at temperature" T If temperature of system increases, then fraction of solid submerged in liquid