A wire AB of length 0.05 m weighting 0.012 kg has its ends resting on two metal plates M, and M₂. The two metal plates are connected to an electric circuit as shown in Fig. 3(a).28 and magnetic fields of strength 1.2 T is applied at right angles to the plane of the paper and is directed into it. It is observed that when the resistance of the circuit falls below 50 ohm, the wire AB starts sliding. Calculate the co-efficient of friction between the wire and the metal plates.
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Answer:
Cross-sectional area of wire A, a
1
=1.0mm
2
=1.0×10
−6
m
2
Cross-sectional area of wire B, a
2
=2.0mm
2
=2.0×10
−6
m
2
Young’s modulus for steel, Y
1
=2×10
11
Nm
−2
Young’s modulus for aluminium, Y
2
=7.0×10
10
Nm
−2
(a) Let a small mass m be suspended to the rod at a distance y from the end where wire A is attached.
Stress in the wire = Force / Area = F / a
If the two wires have equal stresses, then:
F
1
/a
1
=F
2
/a
2
Where,
F
1
= Force exerted on the steel wire
F
2
= Force exerted on the aluminum wire
F
1
/F
2
=a
1
/a
2
=1/2
Sanaya..
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