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  4. A lead bullet of 10 g travelling at 300 m s- 1 strikes against a block of wood comes to rest. Assuming 50 % of heat is absorbed by the bullet, the increase in its temperature (Specific heat of lead = 150 J kg- 1 k- 1 )

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Q. A lead bullet of $10 \, g$ travelling at $300 m \, s^{- 1}$ strikes against a block of wood comes to rest. Assuming $50\%$ of heat is absorbed by the bullet, the increase in its temperature (Specific heat of lead = $150 \, J \, kg^{- 1 \, }k^{- 1}$ )

NTA AbhyasNTA Abhyas 2020

Solution:

Here, $m=10$ g = $10^{- 2}$ kg
$v=300 \, m \, s^{- 1}, \, \Delta \theta =?, \, C=150$ $\text{ J} \text{ k} \, \text{g}^{- 1} \, \, \text{K}^{- 1}$
$Q=\frac{50}{100}\left(\frac{1}{2} m v^{2}\right)=\frac{1}{4}\times \left(10\right)^{- 2}\left(300\right)^{2}=225 \, $ J
From $Q = m C \Delta \theta $
$\theta \, =\frac{Q}{C m}=\frac{225}{150 \times 10^{- 2}}=150 \, ℃$