InterviewSolution
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InterviewSolution
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A body of mass M at rest is struck by a moving body of mass. Prove that the fraction of the initial kinetic energy of mass transferred to the struck body is `(4Mm)/((m+M)^(2))` |
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Answer» Here, `m_(1)=m,u_(1)=u,(say),` `m_(2)=M, u_(2)=0, upsilon_(2)=?` From `upsilon_(2)=(2m_(1)u_(1))/(m_(1)+m_(2))+((m_(2)-m_(1))u_(2))/(m_(1)+m_(2))` `=(2m u)/(m+M)+0=(2m u)/(m+M)` K.E. of the body struck, after collision `E_(2)=(1)/(2)m_(2)v_(2)^(2)=(1)/(2)M((2m u )/(m+M))^(2)=(2Mm^(2)u^(2))/((m+M)^(2))` Initial K.E. of moving body `E_(1)=(1)/(2)m_(1)u_(1)^(2)=(1)/(2)m u^(2)` `:.` Fraction of initial K.E. transferred `(E_(2))/(E_(1))=(2Mm^(2)u^(2))/((m+M)^(2)((1)/(2)m u^(2)))=(4mM)/((m+M)^(2))` |
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