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 $l_1/(l_1 + l_2)$ :-

A lead bullet at $27\,^oC$ just melts when stopped by an obstacle. Assuming that $25\%$ of heat is absorbed by the obstacle, then the velocity of the bullet at the time of striking is …….. $m/s$ ($M.P.$ of lead $= 327\,^oC,$ specific heat of lead $= 0.03\,cal/g\,^oC,$ latent heat of  fusion of lead $= 6\,cal/g$ and $J = 4.2\,joule/cal$ )

On heating a liquid of coefficient of cubical expansion $\gamma $ in a container having coefficient of linear expansion $\gamma /3,$ the level of liquid in the container will

A lead bullet at $27\,^oC$ just melts when stopped by an obstacle. Assuming that $25\%$ of heat is absorbed by the obstacle, then the velocity of the bullet at the time of striking …….. $m/s$ ( $M. P.$ of lead $= 327\,^oC,$ specific heat of lead $= 0.03\,cal/g\,^oC,$ latent heat of fusion of lead $= 6\,cal/g$ and $J = 4.2\,joule/cal$ )

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