A beaker of height $H$ is made up of a material whose coefficient of linear thermal expansion is $3\alpha $ . It is filled up to the brim by a liquid whose coefficient of thermal expansion is $\alpha $. If now the beaker along with its contents is uniformly heated through a small temperature $T$ the level of liquid will reduce by (given $\alpha << 1$)
$5\ \alpha \ TH$
$3\ \alpha \ TH$
$9\ \alpha \ TH$
$8\ \alpha \ TH$
A brass rod of length $50\; cm$ and diameter $3.0 \;mm$ is jotned to a steel rod of the same length and diameter. What is the change in length of the combined rod at $250\,^{\circ} C ,$ if the original lengths are at $40.0\,^{\circ} C ?$ Is there a 'thermal stress' developed at the junction? The ends of the rod are free to expand (Co-efficient of linear expansion of brass $=2.0 \times 10^{-5} \;K ^{-1},$ steel $=1.2 \times 10^{-5}\; K ^{-1} J$
Give the value of coefficient of volume expansion at $0\,^oC$ for ideal gas.
The diagram below shows the change in the length $X$ of a thin uniform wire caused by the application of stress $F$ at two different temperatures $T_1$ and $T_2$. The variation shown suggests that
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
A metallic tape gives correct value at $25^{\circ} C$. A piece of wood is being measured by this metallic tape at $10^{\circ} C$. The reading is $30 \,cm$ on the tape, the real length of wooden piece must be .......... $cm$