$200 \,g$ of ice at $-20^{\circ} C$ is mixed with $500 \,g$ of water at $20^{\circ} C$ in an insulating vessel. Final mass of water in vessel is ........... $g$ (specific heat of ice $=0.5 \,cal g ^{-10} C ^{-1}$ )

A bullet of mass $10 \,g$ moving with a speed of $20 \,m / s$ hits an ice block of mass $990 \,g$ kept on a frictionless floor and gets stuck in it. How much ice will melt if $50 \%$ of the lost KE goes to ice is .......... $g$ (initial temperature of the ice block and bullet $=0^{\circ} C$ )

Heat required to convert $5\ kg$ ice at $0\ ^oC$ into water at $100\ ^oC$ is

A lead bullet penetrates into a solid object and melts. Assuming that $40 \%$ of its kinetic energy is used to heat it, the initial speed of bullet is ............ $ms ^{-1}$

(Given, initial temperature of the bullet $=127^{\circ} C$,

Melting point of the bullet $=327^{\circ} C$,

Latent heat of fusion of lead $=2.5 \times 10^{4} \,J Kg ^{-1}$,

Specific heat capacity of lead $=125 \,J / kg K$ )

$540\, g$ of ice at $0^oC$ is mixed with $540\, g$ of water at $80^oC$. The final temperature of the mixture is

One end of a $2.35\,\,m$ long and $2.0\,\,cm$ radius aluminium rod$(K = 235 \,\,W.m^{-1}K^{-1})$ is held at $20^0\,\,C$. The other end of the rod is in contact with a block of ice at its melting point. The rate in $kg.s^{-1}$ at which ice melts is

[Take latent heat of fusion for ice as $\frac{{10}}{3} ×10^5 J.kg^{-1} $]