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Electromagnetic Induction — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsElectromagnetic Induction5 Marks
Question
The system containing the rails and the wire of the previous problem is kept vertically in a uniform horizontal magnetic field B that is perpendicular to the plane of the rails (figure). It is found that the wire stays in equilibrium. If the wire ab is replaced by another wire of double its mass, how long will it take in falling through a distance equal to its length?
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Answer


Given Blv = mg …(1)
When wire is replaced we have
2mg - Blv = 2ma [where a → acceleration]
$\Rightarrow\text{a}=\frac{2\text{mg}-\text{Blv}}{2\text{m}}$
Now, $\text{s}=\text{ut}+\frac{1}{2}\text{at}^2$
$\Rightarrow\text{l}=\frac{1}{2}\times\frac{2\text{mg}-\text{Blv}}{2\text{m}}\times\text{t}^2 \ \big[\therefore \ \text{s}=\text{l}\big]$
$\Rightarrow\text{t}=\sqrt{\frac{4\text{ml}}{2\text{mg}-\text{Blv}}}=\sqrt{\frac{4\text{ml}}{2\text{mg}-\text{mg}}}=\sqrt{\frac{2\text{l}}{\text{g}}}$ [from (1)]

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