Morning breakfast gives $5000 \,cal$ to a $60 \,kg$ person. The efficiency of person is $30 \%$. The height upto which the person can climb up by using energy obtained from breakfast is ......... $m$

$M$ grams of steam at $100^{\circ} \mathrm{C}$ is mixed with $200\; \mathrm{g}$ of ice at its melting point in a thermally insulated container. If it produces liquid water at $40^{\circ} \mathrm{C}$ [heat of vaporization of water is $540 \;cal/\mathrm{g}$ and heat of fusion of ice is $80 \;\text { cal/g }]$ the value of $\mathrm{M}$ 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 $=125 \,J / kg K$ )

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

In an industrial process $10\, kg$ of water per hour is to be heated from $20^o C$ to $80^o C$ . To do this steam at $200^o C$ is passed from a boiler into a copper coil immersed in water. The steam condenses in the coil and is returned to the boiler as water at $90^o C$. How many kg of steam is required per hour. (Specific heat of steam $= 0.5\, cal/g^o C$, Latent heat of vaporisation $= 540 cal/g)$

When $x\, grams$ of steam at $100\,^oC$ is mixed  with $y\,grams$ of ice at $0\,^oC$ , We obtain $(x + y)\,grams$ of water at $100\,^oC$  . What is the ratio $y/x$ ?