A bullet of mass $10 \mathrm{g}$ moving with speed of $120 \mathrm{m} {\mathrm{s}}^{-1}$ hits an ice block of mass $990 \mathrm{g}$ kept on a frictionless horizontal floor and gets embedded into it. Temperature of ice block is $0°\mathrm{C}$ and its latent heat of fusion is $80$ calorie/gram. If ${\left(\frac{3}{4}\right)}^{th}$ of the energy lost in collision is used into heating the ice, mass of ice melted (in $\mathrm{g}$) is $[1\mathrm{cal}=4.2 \mathrm{J}]$

The figure shows a composite rod made of two different material of thermal conductivity $\left(\frac{K}{4}\right)$ and $K$ respectively. The length of two rods are shown in figure. If the end temperature are $T_1$ and $T_2$ respectively, then the temperature of interface is $\frac{T_1+n{T}_2}{n+1}·$ Value of $n$, is

A brass rod and an aluminium rod each of length $1 \mathrm{m}$ and same cross section area $1{ \mathrm{cm}}^2$ are placed in contact with each other as shown. Temperature of both the rods is raised by $100 K$. The coeffcients of linear expansion of brass and aluminium are $2.0\times {10}^{-5}{ \mathrm{K}}^{-1}$ and $2.4\times {10}^{-5}{ \mathrm{K}}^{-1}$ respectively. If the Young's moduli of brass and aluminium are ${10}^{11} \mathrm{N} {\mathrm{m}}^2$ and $7\times {10}^{10} \mathrm{N} {\mathrm{m}}^2$ respectively then stress in the rods is