1. Tardigrade
  2. Question
  3. Physics
  4. At 30° C, a lead bullet of 50 g, is fired vertically upwards with a speed of 840 m / s. The specific heat of lead is 0.02 cal / g ° C. On returning to the starting level, it strikes a cake of ice at 0° C. The amount of ice melted is (Assume all the energy is spent in melting only latent heat of fusion of ice is 80 cal / g )

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Q. At $30^{\circ} C$, a lead bullet of $50\, g$, is fired vertically upwards with a speed of $840 \,m / s$. The specific heat of lead is $0.02\, cal / g ^{\circ} C$. On returning to the starting level, it strikes a cake of ice at $0^{\circ} C$. The amount of ice melted is (Assume all the energy is spent in melting only \& latent heat of fusion of ice is $80\, cal / g$ )

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Solution:

$m_{b} s_{b}(30-0)+\frac{1}{2} m v^{2}=m_{i c e} L$
$\Rightarrow 50 \times 0.02 \times(30-0)( cal )+\frac{1}{2} \times 50 \times 10^{-3} \times 840 \times 840( J )=m_{i c e} 80( cal )$
$\Rightarrow 30( cal )+\frac{1}{2} \times \frac{50 \times 10^{-3} \times 840 \times 840( cal )}{4.2}=m_{i c e} 80( cal )$
$\Rightarrow m_{i c e}=52.875\, g$