The coefficient of volume expansion of glycerin is $49 \times 10^{-5} \,K ^{-1}$. The fractional change in the density on a $30^{\circ} C$ rise in temperature is ..........
$1.47 \times 10^{-2}$
$1.47 \times 10^{-3}$
$1.47 \times 10^{-1}$
$1.47 \times 10^{-4}$
A brass disc fits simply in a hole of a steel plate. The disc from the hole can be loosened if the system
Two rods $A$ and $B$ of identical dimensions are at temperature $30\,^oC$. If a heated upto $180\,^oC$ and $B$ upto $T\,^oC$, then the new lengths are the same. If the ratio of the coefficients of linear expansion of $A$ and $B$ is $4:3$, then the value of $T$ is........$^oC$
The coefficient of linear expansion of crystal in one direction is ${\alpha _1}$ and that in every direction perpendicular to it is ${\alpha _2}$. The coefficient of cubical expansion is
Three rods of equal length $l$ are joined to form an equilateral triangle $PQR.$ $O$ is the mid point of $PQ.$ Distance $OR$ remains same for small change in temperature. Coefficient of linear expansion for $PR$ and $RQ$ is same i.e. ${\alpha _2}$ but that for $PQ$ is ${\alpha _1}$. Then relation between ${\alpha _1}$ and ${\alpha _2}$ is
Coefficient of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$. Lengths of brass and steel rods are $l_1$ and $l_2$ respectively. If $\left(l_2-l_1\right)$ is maintained same at all temperatures, which one of the following relations holds good?