The coefficient of volume expansion of glycerin is $49 \times 10^{-5} \,K ^{-1}$. The fractional change in the density on a $30^{\circ} C$ rise in temperature is ..........

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 $\frac{{{l_1}}}{{({l_1} + {l_2})}}$

Write relation between $\alpha _l,\,\alpha _A$ and $\alpha _V$.

Find out the increase in moment of inertia $I$ of a uniform rod (coefficient of linear expansion a) about its perpendicular bisector when its temperature is slightly increased by $\Delta T$.

When vapour condenses into liquid

A glass flask of volume one litre at $0^oC$ is filled, level full of mercury at this temperature. The flask and mercury are now heated to $100°C$ ........... $cc$ mercury will spill out, if coefficient of volume expansion of mercury is $1.82 \times {10^{ - 4}}°C^{-1}$ and linear expansion of glass is $0.1 \times {10^{ - 4}}°C^{-1}$ respectively