Answer :

Given:


Initial mass = m


Magnetic field = B


Length of sliding wire = l


Formula used:


Magnetic force … (i), where i = current, l = length of sliding wire, B = magnetic field.


At equilibrium, this magnetic force balances the weight of the wire mg acting downward, where m = mass, g = acceleration due to gravity.


Therefore, … (ii)


Now, when the wire ab is replaced by another wire of mass 2m, the weight acting downward will be 2mg, where g = acceleration due to gravity.


Hence, net force = 2mg - ilB … (iii) where 2m = mass, g = acceleration due to gravity, i = current, l = length of sliding wire, B = magnetic field.


According to Newton’s law of motion, … (iv), where F = net force, m’ = mass, acceleration


In this case, m’ = 2m.


Therefore, equating (iii) and (iv), we get


2mg - ilB = 2ma


(v)


Now, distance travelled can be expressed as … (vi), where s = distance travelled, u = initial velocity = 0(in this case), t = time, a = acceleration.


Now, distance travelled = l (given)


Therefore, from (v), (vi) becomes:




But, from (i),


Therefore,


Required time taken = (Ans)


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