Work Energy Power

JEE Main level, single correct, medium

84 of 183

Question 84 of 183

A bag of sand of mass 9.8kg9.8kg is suspended by a rope. AA bullet of 200g200g travelling with speed 10ms−110{ms}^{-1} gets embedded in it, then loss of kinetic energy will be

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Answer: (B) 9.8J9.8J

If the final velocity of the bullet and the bag is vv, applying conservation of momentum,
mu=(m+M)v⇒0.2×10=(0.2+9.8)v⇒v=0.2ms−1mu=\left(m+M\right)v \Rightarrow 0.2\times 10=\left(0.2+9.8\right)v \Rightarrow v=0.2m{s}^{-1}
Loss in kinetic energy will be,
Ki−Kf=(12×0.2×102)−(12×10×0.22)=9.8J{K}_{i}-{K}_{f}=\left(\dfrac{1}{2}\times 0.2\times {10}^{2}\right)-\left(\dfrac{1}{2}\times 10\times 0.{2}^{2}\right)=9.8J

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