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 $=125 \,J / kg K$ )

$0.1\,m^3$ of water at $80\,^oC$ is mixed with $0.3\,m^3$ of water at $60\,^oC$. The final temperature of the mixture is ........ $^oC$

Heat needed to convert $1$ kilogram ice at $0^o\,C$ to steam at $100^o\,C$ is

Steam at $100°C$ is passed into $1.1\, kg$ of water contained in a calorimeter of water equivalent $0.02 \,kg$ at $15°C$ till the temperature of the calorimeter and its contents rises to $80°C.$ The mass of the steam condensed in $kg$ is 

$500\, g$ of water and $100\, g$ of ice at $0\,^oC$ are in a calorimeter whose water equivalent is $40\, g$. $10\, g$ of steam at $100\,^oC$ is added to it. Then water in the calorimeter is ....... $g$ (Latent heat of ice $\,= 80\, cal/g$, Latent heat of steam $\,= 540\, cal/ g$)

If mass energy equivalence is taken into account, when water is cooled to form ice, the mass of water should