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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» At any time , let the velocity of the rod be v . Applying Newtons law: F-iIB=ma…..(1) Also `Biv=i_(1)R=(q)/( c)` Applying Kcl, `i=i_(1)+(dq)/(dt)=(BlV)/( R)+(D)/(Dt)(BIvC) or i=(B l V)/( R)+B l C 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)(v)/(F-(B^(2)I^(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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