Two rods, one of aluminum and the other made of steel, having initial length ${l_1}$ and ${l_2}$ are connected together to form a single rod of length ${l_1} + {l_2}$. The coefficients of linear expansion for aluminum and steel are ${\alpha _a}$ and ${\alpha _s}$ respectively. If the length of each rod increases by the same amount when their temperature are raised by ${t^o}C$, then find the ratio $\frac{{{l_1}}}{{({l_1} + {l_2})}}$
$\frac{{{\alpha _s}}}{{{\alpha _a}}}$
$\frac{{{\alpha _a}}}{{{\alpha _s}}}$
$\frac{{{\alpha _s}}}{{({\alpha _a} + {\alpha _s})}}$
$\frac{{{\alpha _a}}}{{({\alpha _a} + {\alpha _s})}}$
The coefficient of linear expansion of brass and steel are ${\alpha _1}$ and ${\alpha _2}$. If we take a brass rod of length ${l_1}$ and steel rod of length ${l_2}$ at $0°C$, their difference in length $({l_2} - {l_1})$ will remain the same at a temperature if
At what temperature (in $ ^{\circ} C$) a gold ring of diameter $6.230$ $cm$ be heated so that it can be fitted on a wooden bangle of diameter $6.241 \,cm$ ? Both the diameters have been measured at room temperature $\left(27^{\circ} C \right)$. (Given: coefficient of linear thermal expansion of gold $\alpha_{L}=1.4 \times 10^{-5} \,K ^{-1}$ )
Two rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature will be
( ${\alpha _1},\,{\alpha _2},$ = linear expansion coefficient
$A_1, A_2$ = Area of rods
$Y_1, Y_2$ = Young modulus)
A piece of metal weight $46\, gm$ in air, when it is immersed in the liquid of specific gravity $1.24$ at $27°C$ it weighs $30\, gm.$ When the temperature of liquid is raised to $42°C$ the metal piece weight $30.5\, gm,$ specific gravity of the liquid at $42°C$ is $1.20,$ then the linear expansion of the metal will be
Give name of substance that contracts with increase in temperature.