At 30^∘ C, a lead bullet of 50 g, is fired vertically upwards with a speed of 840 m / s. The s

step 1 Hello students in this question we have given that at temperature T1 equals to 30 degree centigr

At 30^∘ C, a lead bullet of 50 g, is fired vertically...

At $30^{\circ} \mathrm{C}$, a lead bullet of $50 \mathrm{~g}$, is fired vertically upwards with a speed of $840 \mathrm{~m} / \mathrm{s}$. The specific heat of lead is $0.02 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}$. On returning to the starting level, it strikes to a cake of ice at $0^{\circ} \mathrm{C}$. The amount of ice melted is: (Assume all the energy is spent in melting only) (a) $62.7 \mathrm{~g}$ (b) $55 \mathrm{~g}$ (c) $52.875 \mathrm{~kg}$ (d) $52.875 \mathrm{~g}$

At $30^{\circ} \mathrm{C}$, a lead bullet of $50 \mathrm{~g}$, is fired vertically upwards with a speed of $840 \mathrm{~m} / \mathrm{s}$. The specific heat of lead is $0.02 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}$. On returning to the starting level, it strikes to a cake of ice at $0^{\circ} \mathrm{C}$. The amount of ice melted is:
(Assume all the energy is spent in melting only)
(a) $62.7 \mathrm{~g}$
(b) $55 \mathrm{~g}$
(c) $52.875 \mathrm{~kg}$
(d) $52.875 \mathrm{~g}$

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Key Concepts

Conservation of Energy

This principle states that energy cannot be created or destroyed, only transformed from one form to another. In problems like these, the total mechanical energy (including both kinetic and potential forms) of the moving object is ultimately converted into thermal energy, which can then be used to induce physical changes such as melting.

Energy Transformation in Projectile Motion

When an object is projected vertically, its kinetic energy is converted into gravitational potential energy as it ascends and then back to kinetic energy as it descends. Upon impact, assuming negligible losses elsewhere, this mechanical energy is transformed into heat energy, which can be harnessed to drive processes like a phase change.

Latent Heat of Fusion

Latent heat of fusion is the amount of heat energy required per unit mass to change a substance from a solid to a liquid at its melting point without a temperature change. It provides the direct connection between the heat energy supplied (from the transformed mechanical energy) and the mass of the ice melted.

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