InterviewSolution
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InterviewSolution
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Two small balls A and B each of mass m, are joined rigidly to the ends of a light rod of length L figure. The system translates on a frictionless horizontal surface with a velocity `v_0` in a direction perpendicular to the rod. A particle P of mass kept at rest on the surface sticks to the ball A as the ball collides with it . Find a. the linear speeds of the balls A and B after the collision, b. the velocity of the centre of mass C of the system A+B+P and c. the angular speed of the system about C after the collision. |
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Answer» Correct Answer - A::B::C::D Two ball A and B each of mass m are joined rigidly to the ends of a light rod of length L. The system moves with a velocity `V_0` in a direction perpendicular to the rod. A particle P of mass m kept at rest rod. A particle OP of masss m kept at rest on teh surface sticks to the ball A as the ball collides with it. a. The light rod wil exert a force on the bal B only along its length. So collision will not affect its velocity. B has a velocity `=V_0` if we consider the three bodies to be a system Applying L.C.L.M. Therefore `mv_0=2mxxv` `rarr v=v_0/2` Therefore A has velocity `=v_0/2` b. If we consider the three bodies tobe a system net exterN/Asl force =0` Therefore `V_(VCM)=(mxxv_0+2mxx(v_0/2))/(m+2m)` ltbr.gt `=(mv_0+mv_0)/(3m)` `=(2v_0)/3` (along the iniltial velocity as befoe collision) c. The velocity of (A+P) w.r.t `the center of pass ={((2v_0)/3)}-(v_0-2)` `=v_0/6` and the velocity of B w.r.t the centre of mass `=v_0-(2v-0)/3=v_0/3` (only magnitude has been taken) Distance of the (A+P) from centre of mass `=l/3 and for B it is ((2l)/3)` therfore `P_(cm)=L_(cm)xxomega` `rarr 2mxxV_0/6xxl/3+mxxV_0/3xx(2l)/3 `{2m(l/3)^2+((2l)/3)^2m}xxomega` rarr 6m(V_0l)/18=18((6ml)/9)omega` `rarr omega=(v_0/(2l))` |
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