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  4. A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of 60 ms -1. What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail? [Specific heat capacity of iron =0.42 Jg -1 ° C -1 ]

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Q. A $100\, g$ of iron nail is hit by a $1.5\, kg$ hammer striking at a velocity of $60\, ms ^{-1}$. What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail? [Specific heat capacity of iron $=0.42\, Jg ^{-1}{ }^{\circ} C ^{-1}$ ]

JEE MainJEE Main 2022Thermal Properties of Matter

Solution:

$\begin{array}{l} \text { Heatenergy }=\frac{1}{4} \times \text { Kinetic energy } \\ m c \Delta T=\frac{1}{4} \times \frac{1}{2} m v^2 \\ 0.1 \times 420 \times \Delta T=\frac{1}{8} \times 1.5 \times(60)^2 \\ \Delta T=\frac{1}{8} \times \frac{1.5 \times(60)^2}{0.1 \times 420} \\ \Delta T=\frac{5400}{336} \\ \Delta T=16.07^{\circ} C \end{array}$