$A$ hunter fired a metallic bullet of mass $m \ kg$ from a gun towards an obstacle and it just melts when it is stopped by the obstacle. The initial temperature of the bullet is $300 \ K$. If $\frac{1}{4}$ th of the heat is absorbed by the obstacle,then the minimum velocity of the bullet is (Melting point of bullet $= 600 \ K$,Specific heat of bullet $= 0.03 \ cal \ g^{-1} {}^{\circ} C^{-1}$,Latent heat of fusion of bullet $= 6 \ cal \ g^{-1}$) (in $ms^{-1}$)

  • A
    $410$
  • B
    $260$
  • C
    $460$
  • D
    $310$

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Similar Questions

Match the following List-$I$ with List-$II$.
List-$I$List-$II$
$A$. When ice melts into water$I$. Volume increases
$B$. When water changes into steam$II$. Volume decreases
$C$. Melting point of ice$III$. Increases with increase of pressure
$D$. Boiling point of water$IV$. Decreases with increase in pressure

Match List-$I$ with List-$II$.
List-$I$List-$II$
$(A)$ Heat capacity of body$(I)$ $J kg^{-1}$
$(B)$ Specific heat capacity of body$(II)$ $J K^{-1}$
$(C)$ Latent heat$(III)$ $J kg^{-1} K^{-1}$
$(D)$ Thermal conductivity$(IV)$ $J m^{-1} K^{-1} s^{-1}$

Choose the correct answer from the options given below:

$A$ refrigerator converts $500\,g$ of water at $25\,^{\circ}C$ into ice at $-10\,^{\circ}C$ in $3\,hours\,40\,minutes$. The quantity of heat removed per minute is ........ $cal/\min$.
(Specific heat of water $= 1\,cal/g\,^{\circ}C$,Specific heat of ice $= 0.5\,cal/g\,^{\circ}C$,Latent heat of fusion $= 80\,cal/g$)

$A$ beaker of height $H$ is made up of a material whose coefficient of linear thermal expansion is $3\alpha$. It is filled up to the brim by a liquid whose coefficient of thermal expansion is $\alpha$. If now the beaker along with its contents is uniformly heated through a small temperature $T$,the level of liquid will reduce by (given $\alpha T << 1$):

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$A$ geyser heats water flowing at the rate of $3.0 \, L/min$ from $27 \, ^{\circ}C$ to $77 \, ^{\circ}C$. If the geyser operates on a gas burner,what is the rate of consumption (in $g/min$) of the fuel if its heat of combustion is $4.0 \times 10^{4} \, J/g$?

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