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Q.

Two long smooth conducting rails separated by distance l  are fixed in vertical plane as shown in figure. The lower ends of the rails are connected by a resistor R. Another conducting rod PQ is allowed to move smoothly and vertically on conducting rails. The entire region is having horizontal uniform magnetic field B which is directed into the plane of paper. The rod is imparted an initial velocity u in upward direction. Assuming no resistance is present other than R and acceleration due to gravity is g, mark the correct statement(s).

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a

The speed of rod first decreases, becomes zero at an instant and then increases and finally attains a constant value.

b

The magnitude of acceleration of rod is continuously decreasing without any change in its direction and finally becomes zero. 

c

The acceleration of rod is constant.

d

The magnitude of acceleration of rod is first decreasing, becomes minimum and then increases but direction of acceleration remains same.

answer is A, D.

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Detailed Solution

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B2l2vR+mg a=g+B2l2vmR

As it goes up velocity decreases and hence acceleration decreases. When velocity is zero,  a=g. Then the rod comes down with increasing velocity till it achieves terminal velocity. ‘a’ remains downward and decreases to zero.

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