A glass flask of volume one litre at $0^oC$ is filled, level full of mercury at this temperature. The flask and mercury are now heated to $100°C$ ........... $cc$ mercury will spill out, if coefficient of volume expansion of mercury is $1.82 \times {10^{ - 4}}°C^{-1}$ and linear expansion of glass is $0.1 \times {10^{ - 4}}°C^{-1}$ respectively
A metallic rod $1\,cm$ long with a square cross-section is heated through $1^o C$. If Young’s modulus of elasticity of the metal is $E$ and the mean coefficient of linear expansion is $\alpha$ per degree Celsius, then the compressional force required to prevent the rod from expanding along its length is :(Neglect the change of cross-sectional area)
On heating a uniform metallic cylinder length increases by $3 \%$. The area of cross-section of its base will increase by ........... $\%$
A steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5}$ $mm$ at a certain temperature. The maximum temperature variation allowable during the ruling is .......... $^oC$ (Coefficient of linear expansion of steel $ = 10 \times {10^{ - 6}}{K^{ - 1}})$
The gap between any two rails, each of length $l$ laid on a railway track equal $x$ at $27\,^oC$ . When the temperature rises to $40\,^oC$ , the gap close up. The coefficient of linear expansion of the material of the rail is $\alpha $ . The length $l$ of a rail at $27\,^oC$ will be