The coefficient of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are ${\gamma _1}$ and ${\gamma _2}$  respectively. If the coefficient of linear expansion of vessel $A$ is $\alpha $, the coefficient of linear expansion of vessel $B$ is

Two rods, one made of aluminium and the other made of steel, having initial lengths $l_1$  and $l_2$ respectively are connected together to form a single rod of length $(l_1 + l_2)$. The coefficients of linear expansion for aluminium and steel of $\alpha_1$ and $\alpha_2$ respectively. If the length of each rod increases by the same amount when  their temperature is raised by $t^oC$, then the ratio $l_1/(l_1 + l_2)$ :-

Steam at $100\,^oC$ is passed into $1.1\,kg$ of water contained in calorimeter of water equivalent $0.02\ kg$ at $15\,^oC$ till the temperature of the calorimeter rises to $80\,^oC$. The mass of steam condensed in kilogram is

The coefficient of apparent expansion of mercury in a glass vessel is $153\times 10^{-6}/\,^oC$ and in a steel vessel is $144\times 10^{-6}/\,^oC.$ If $\alpha $ for steel is $12 \times 10^{-6}/\,^oC,$ then $\alpha $ that of glass is

A bullet moving with a uniform velocity v, stops suddenly after hitting the target and the whole mass melts be $m$, specific heat $S,$ initial temperature $25°C$ melting point $ 475°C$ and the latent heat $L.$ Then $v$ is given by