NEET Sample Paper NEET Sample Test Paper-73

  • question_answer
    A bomb of mass 3.0 kg explodes in air into two pieces of masses 2.0 kg and 1.0 kg. The smaller mass goes at a speed of 80 m/s. The total energy imparted to the two fragments is

    A) 1.07 kJ             

    B) 2.14 Kj

    C) 2.4 kJ               

    D) 4.8 kJ

    Correct Answer: D

    Solution :

    From the law of conservation of momentum, when no external force acts upon a system of two (or more) bodies, then the total momentum of the system remains constant. Momentum before explosion = momentum after explosion Since bomb v at rest, its velocity is zero, hence \[\operatorname{mv}={{m}_{1}}{{\nu }_{1}}\,\,+\,\,{{m}_{2}}{{\nu }_{2}}\] \[3\,\,\times \,\,0\,\,=\,\,2{{\nu }_{1}}+1\,\,\times \,\,80\] \[\Rightarrow \,\,\,\,\,{{\nu }_{1}}=-\frac{80}{2}\,\,=\,\,-\,40\,m/s\] Total energy imparted is \[KE=\frac{1}{2}{{m}_{1}}\nu _{1}^{2}+\frac{1}{2}{{m}_{2}}\nu _{2}^{2}\] \[=\,\,\,\frac{1}{2} \times \,\,2\,\,\times \,\,{{\left( -\,40 \right)}^{2}}\,\,+\,\,\frac{1}{2}\,\,\times \,\,1\,\,\times \,\,{{\left( 80 \right)}^{2}}\] \[= 1600+3200= 4800 J\] \[=\text{ }4.8\text{ }kJ\] Note: Since velocity of second piece is negative, it indicates that the piece is moving in opposite direction to the direction of the other piece.


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