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Work, Energy, and Power — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsWork, Energy, and Power2 Marks
Question
A bullet of mass 0.012kg and horizontal speed $70ms^{-1}$ strikes a block of wood of mass 0.4kg and instantly comes to rest with respect to block. The block is suspended from the ceiling by means of thin wires. Calculate the height to which the block rises.
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Answer

Mass of the bullet ($m_0$) = 0.012kg Mass of a block of the wood (M) = 0.4kg Horizontal speed of the bullet (u) = $70ms^{-1}$ Let V is the velocity of combination, then by conservation of linear momentum. $\text{V}=\frac{\text{m}_0\text{u}}{\text{m}_0+\text{M}}=\frac{0.012\times70}{0.012+0.4}$ $=\frac{0.84\text{ms}^{-1}}{0.412}=2.04\text{ms}^{-1}$ Let h be the height through which the block rises. Then from the conservation of energy P.E. of the combination = K.E. of the combination.$\Rightarrow(\text{M}+\text{m}_0)\text{gh}=\frac{1}{2}(\text{M}+\text{m}_0)\text{V}^2$
$\Rightarrow\text{h}=\frac{\text{V}^2}{2\text{g}}$ $\Rightarrow\text{h}=\frac{(2.04)^2}{2\times9.8}=\frac{4.1616}{19.6}$ $=0.212\text{m}$

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