# The system

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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