InterviewSolution
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InterviewSolution
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Two masses `nm` and `m`, start simultaneously from the intersection of two straight lines with velocities `v` and `nv` respectively. It is observed that the path of their centre of mass is a straight line bisecting the angle between the given straight lines. Find the magnitude of the velocity of centre of mass. [Here `theta=`angle between the lines] |
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Answer» `vecv_(cm)=(m_(1)vecv_(1)+m_(1)vecv_(2))/(m_(1)+m_(2))` `vecv_(cm)=(nmvhati+mnvcosthetahati+nmv sin theta hatj)/(m+nm)` `v_(cm)=sqrt((nmv+mnvcostheta)^(2)+(nmvsintheta)^(2))/(m(1+n))` `v_(cm)=(nmvsqrt((1+costheta)^(2)+(sintheta)^(2)))/(m(1+n))` `=(nvsqrt(1+cos^(2)theta+2costheta+sin^(2)theta))/((1+n))` `=((nv)/(n+1))sqrt(2costheta/2)` `v_(cm)=(2nv"cos" theta/2)/(n+1)` |
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