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  4. A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed 10 ms -1 gets embedded in it, then loss of kinetic energy will be

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Q. A bag of sand of mass $9.8\, kg$ is suspended by a rope. A bullet of $200\, g$ travelling with speed $10\, ms ^{-1}$ gets embedded in it, then loss of kinetic energy will be

JEE MainJEE Main 2022Work, Energy and Power

Solution:

$ P_{ i }=P_{ f }$ ( no any external force )
$ 0.2 \times 10=10 \times v$
$ v =0.2 \,m / sec $
Loss in K.E. $=\frac{1}{2} \times(0.2) \times 10^2-\frac{1}{2} \times 10(0.2)^2 $
$ =\frac{1}{2} \times 10 \times(0.2)[10-0.2] $
$ =9.8\, J $