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)
$EA\alpha t$
$EA\alpha t/(1 + \alpha t)$
$EA\alpha t/(1\alpha t)$
$E/\alpha t$
The coefficient of volume expansion of glycerin is $49 \times 10^{-5} \;K ^{-1} .$ What is the fractional change in its density for a $30\,^{\circ} C$ rise in temperature?
A cylindrical metal rod of length $L_0$ is shaped into a ring with a small gap as shown. On heating the system
A surveyor's $30$-$m$ steel tape is correct at some temperutre. On a hot day the tape has expanded to $30.01$ $m$. On that day, the tape indicates a distance of $15.52$ $m$ between two points. The true distance between these points is :-
The value of coefficient of volume expansion of glycerin is $5 \times 10^{-4}k^{-1} .$ The fractional change in the density of glycerin for a rise of $40^o C$ in its temperature, is
An aluminium sphere of $20 \;cm$ diameter is heated from $0^{\circ} C$ to $100^{\circ} C$. Its volume changes by (given that coefficient of linear expansion for aluminium $\alpha_{A l}=23 \times 10^{-6}\;/{^o}C$