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Consider a perfectly conducting uniform disc of mass m and radius 'a' hinged in a vertical plane from its centre and free to rotate with respect to hinge. A resistance R is connected between centre of the disc annd periphery by using two sliding contacts C_(1) & C_(2). A long non -conducting massless string is wrapped around the disk, whose another end is attached with a block of mass m. There exists a uniform horizontal magnetic field B, whose arrangement is shown in figure. Given system is released from rest at t=0. Assume friction between string and disc is sufficient so that there is no slipping between them let at any instant t, velocity of block is v, angular velocity of the disc is omega and current in resistance is i Just after t=0 the acceleration of block is: |
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Answer» `g` `mgv=mv(DV)/(dt)+I(omega d omega)/(dt)+i^(2)R`………..i `v=aomega` `(dv)/(dt)=a(domega)/(dt)` `i=(Bomegaa^(2))/(2R)=(Bva)/(2R)`………ii From equation i and ii `(3M)/2 (dv)/(dt)=mg-(B^(2)a^(2))/(6mR) v` `v=(4mgR)/(B^(2)a^(2)) (1-e^(-((B^(2)a^(2))/(6mr))t))` `(dv)/(dt)=(2g)/3 e^(-(B^(2)a^(2))/(6mR)t)` 
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