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Find the velocity of the moving rod at time t if the initial velocity of the rod is v and a constant force F is applied on the rod.Neglect the resistance of the rod. |
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Answer» Solution :At any time `t`, let the velocity of the rod be `v`. Applying Newtons law:`F-ilB=ma` ..(1) Also `Blv=i_(1),R=q/c` Applying `KCL`, `i=i_(1)+(dq)/(dt)=(BlV)/R+d/(dt)(BlvC)` or `i=(BlV)/R+BlC a` Putting the VALUE of `i` in eq.(1), `F-(B^(2)L^(2)V)/R=(m+B^(2)L^(2)C)a=(m+B^(2)L^(2)C)(dv)/(dt)` `(m+B^(2)L^(2)C)(dv)/(F-(B^(2)L^(2)V)/R)=dt` Integrating both sides, and solving we get `v=(FR)/(B^(2)l^(2))(1-e(tB^(2)l^(2))/(R(m+CB^(2)l^(2))))` 
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