A current carrying loop is in the shape of an equilateral triangle of side length a. It's mass is M and it is in vertical plane. There exists a uniform horizontal magnetic field B→ of magnitude B0 in the region (up to dotted line) as shown in the diagram. (neglect emf induced in the loop)

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If the loop is in equilibrium for y=34 a, the corresponding current in the loop is 2MgaB0

If the loop is in equilibrium for y=34 a, the corresponding current in the loop is MgaB0

If the loop is displaced slightly from it's equilibrium position y=34a in it's plane perpendicular to side AB and released, the time period of it's oscillation is 2π3a4g

If the loop is displaced slightly from it's equilibrium position y=34a in it's plane perpendicular to side AB and released, the time period of it's oscillation is 2π3a2g

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Detailed Solution

Effective length of loop DABE is line joining DE.ℓe=2ytan⁡30∘=2y3If y=3a4then ℓe=23×3a4=a2 At equilibrium iℓeB0=Mg⇒i=2MgaB0 When it is displaced slightly : dF=iB0dℓ=−2MgaB0×B0×23dy=−4Mg3adyMa=−4Mg3adycomparing with angular SHM a=-ω2yω2=4g3a⇒2πT=4g3a∴T=2π3a4g

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