$A$ surveyor's $30$-$m$ steel tape is correct at some temperature. 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: (in $m$)

$A$ circular disc with a hole is shown in the figure. On heating,if the outer diameter $d_1$ increases by $0.3\%$,then the inner diameter $d_2$ will

$A$ composite rod made up of two rods $AB$ and $BC$ are joined at $B$. The rods are of equal length at room temperature and have equal masses. The coefficient of linear expansion $\alpha$ of $AB$ is more than that of $BC$. The composite rod is suspended horizontally by means of a thread at $B$. When the rod is heated:

The temperature of a metallic sphere of radius $R$ is increased by a small amount $\Delta T$. If the linear coefficient of thermal expansion of the metal is $\alpha$, the approximate increase in the volume of the sphere is :

$A$ copper rod of $88\; cm$ and an aluminum rod of unknown length have their increase in length independent of increase in temperature. The length of the aluminum rod is....$cm$.
$(\alpha_{Cu} = 1.7 \times 10^{-5}\; K^{-1}$ and $\alpha_{Al} = 2.2 \times 10^{-5}\; K^{-1})$

$A$ steel tape measures the length of a copper rod as $90 \ cm$ when both are at $10 \ ^oC$. What length (in $cm$) would the tape read for the length of the rod when both are at $30 \ ^oC$? $[\alpha_{st} = 1.2 \times 10^{-5} / ^oC$ and $\alpha_{cu} = 1.7 \times 10^{-5} / ^oC]$