Question

# Consider two parallel, conducting frictionless tracks are kept in gravity free space as shown in the figure. A movable conductor PQ, initially kept at OA, given a velocity 10 ms−1 towards right. If space contains a magnetic field upon the distance moved by conductor PQ from OA line and given by →B=cx(−^k)[c=constant=1 S.I. unit]. The mass of conductor PQ is 1 kg and length of PQ is 1 m. Answer the following questions based on above passage.

A
The distance travelled by conductor when its speed is 5 ms1 is (102)13m
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B
The heat loss during the time interval t=0 to time t sec, when the speed of conductor is 5 ms1 is 50 J
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C
The distance travelled by conductor when its speed is 5 ms1 is(152)13m
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D
The heat loss during the time interval t=0 to time t sec, when the speed of conductor is 5 ms1 is 10 J
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Solution

## The correct option is C The distance travelled by conductor when its speed is 5 ms−1 is(152)13memf=dϕdt=ddt∫x0BdA+AdBdte=ddt∫x0lxdx+lxdxdte=xvl+xvl=2xvl Current through resistance is I=2xvlR Magnetic force is F=IBl=2x2vl2R Now F=ma a=−vdvdx=2x2vl2mR Applying limits −∫510dv=∫x02x2l2mRdx ⇒+5=2l2mRx33 ⇒x=(152)13…(a) Heat produced in ′R′= loss of kinetic energy of rod H=12×1×(10)2- 12×1×(5)2 H=12[100−25]=752 J Ans : (1)

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