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  • A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of  What will be the rise

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}]

Option: 1

675^{\circ}C


Option: 2

1600^{\circ}C


Option: 3

16.07^{\circ}C


Option: 4

6.75^{\circ}C


Answers (1)

best_answer

\begin{array}{l} K E \text { of hammer }=\frac{1}{2} m v^{2} \\ \\ =\frac{1}{2} \times 1.5 \times(60)^{2} \\ \\ =\frac{3}{4} \times 3600 \\ \\ =2700 \mathrm{~J} \\ \\ \text { Energy given to nail }=\frac{1}{4}(\mathrm{KE} \text { of hammer) } \\ \\ m C \Delta T=\frac{2700}{4} \\ \\ 100 \times 0.42 \times \Delta T=\frac{2700}{4} \\ \\ \Delta T=\frac{2700}{4 \times 42} \\ \\ \Delta T=16.07^{\circ} \mathrm{C} \end{array} \\ \\ \text{The correct option is} (3)

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