A block of ice of mass $M=13.44 \mathrm{kg}$ slides on a horizontal surface. It starts with a speed of $v=10 \mathrm{m}/\mathrm{s}$ and finally stops after moving a distance of $s=30 \mathrm{m}$. What is the mass of ice (in grams) that has melted due to friction between the block and the surface? Latent heat of fusion of ice is $L_{\mathrm{f}}=80 \mathrm{cal}/\mathrm{g}$

This question contains Statement 1 and Statement 2 Of the four choices given after the statements, choose the one that best describes the two statements.

Statement 1: The temperature dependence of resistance is usually given as $R=R_0\left(1+\alpha \mathrm{\Delta }t\right)$. The resistance of a wire changes from $100 \mathrm{\Omega }$ to $150 \mathrm{\Omega }$ when its temperature is increased from $27°\mathrm{C}$ to $227°\mathrm{C}$. This implies that $\alpha =2.5\times {10}^{-3}/{}^{\circ }\mathrm{C}$.

Statement 2: $R=R(1+\alpha \mathrm{\Delta }T)$ is valid only when the change in the temperature $\mathrm{\Delta }T$ is small and $\mathrm{\Delta }R=\left(R-R_0\right)<<R_0$.

A wooden wheel of radius $R$ is made of two semicircular parts (see figure). The two parts are held together by a ring made of a metal strip of cross sectional area $S$ and length $L$. $L$ is slightly less than $2\pi R$. To fit the ring on the wheel, it is heated so that its temperature rises by $\mathrm{\Delta }T$ and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$, and its Young's modulus is $Y$, the force that one part of the wheel applies on the other part is

An external pressure $P$ is applied on a cube at $0°\mathrm{C}$ so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and $\alpha$ is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by: