A wooden cubical block ABCDEFGO of mass m and side 'a' is wrapped by a square wire loop of perimeter 4 a at a /2 as shown. The current in the wire I. The whole system is placed on frictionle

Question

A wooden cubical block ABCDEFGO of mass $m$ and side 'a' is wrapped by a square wire loop of perimeter 4 a at $a /2$ as shown. The current in the wire I. The whole system is placed on frictionless horizontal surface in a uniform magnetic field $B = B_{0} \hat{j}$ . In this situation , normal force between horizontal surface and block passes through a point at a distance $x$ from centre. Select the correct statement(s)

TestHub · Accepted Answer

For rotation equilibrium, taking torque about the point from where normal force passes.

$\frac{a}{2} \times laB_{0} + laB_{0} \frac{a}{2} - mgx = 0 x = \frac{la ^{2} B _{0}}{mg}$

For the block not to topple $x < \frac{a}{2} \Rightarrow 1 < \frac{mg}{2 aB _{0}}$

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JEE Advanced (2028)