To determine the direction of the induced current in the metallic loop when the electric current flows from B to A in the wire, we can use Lenz's law.

Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it.

In this scenario, as the electric current flows from B to A in the wire, it generates a magnetic field around the wire. This magnetic field intersects with the metallic loop.

To oppose the increase in magnetic flux caused by the current flowing from B to A, the induced current in the metallic loop will flow in such a way that it generates its own magnetic field, opposing the external magnetic field produced by the wire.

Using the right-hand rule for the direction of the induced current, if we imagine the magnetic field lines produced by the wire pointing into the page, the induced current will flow in such a direction as to create a magnetic field out of the page.

Therefore, the induced current in the metallic loop will flow counterclockwise when viewed from above. This counterclockwise current flow will generate a magnetic field out of the page, opposing the increase in magnetic flux caused by the current flowing from B to A in the wire.

When two spherical bobs, one metallic and the other glass, of the same size are allowed to fall freely from the same height above the ground, the metallic bob would typically reach the ground earlier than the glass bob.

This difference in falling time arises due to the difference in density between the two materials. Metals generally have higher densities compared to glass. When objects of the same size but different densities fall freely, the one with higher density (metallic bob in this case) experiences greater gravitational force because gravitational force is directly proportional to mass.

Since the metallic bob has a greater mass due to its higher density, it experiences a greater gravitational force and falls faster compared to the glass bob, which has a lower density. Therefore, the metallic bob would reach the ground earlier than the glass bob.

When the flexible wire of irregular shape, ABED, turns into a circular shape and is placed in a region with a magnetic field directed normal to the plane of the loop and away from the reader, the magnetic flux through the loop changes. According to Faraday's law of electromagnetic induction, this change in magnetic flux induces an electromotive force (emf) and consequently an induced current in the loop.

To determine the direction of the induced current in the wire loop, we can use Lenz's law.

Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it.

In this case, as the wire loop is placed in the magnetic field directed away from the reader, the magnetic flux through the loop increases. To oppose this increase in magnetic flux, the induced current will flow in such a direction as to create a magnetic field opposing the external magnetic field.

Using the right-hand rule for the direction of induced current, if we imagine the magnetic field lines pointing away from us (as mentioned in the question), the induced current will flow in such a way that it generates a magnetic field opposing the external magnetic field.

Therefore, the induced current in the wire loop will flow counterclockwise when viewed from the top. This counterclockwise current flow will generate a magnetic field into the plane of the loop, opposing the increase in magnetic flux caused by placing the loop in the external magnetic field.

Lenz's law states that the direction of the induced electromotive force (emf) in a circuit is such that it opposes the change in magnetic flux that produced it.

When a metallic rod is held horizontally along the east-west direction and allowed to fall under gravity, there will be an emf induced at its ends. This is because, as the rod falls, it cuts the Earth's magnetic field lines, resulting in a change in magnetic flux through the rod. According to Faraday's law of electromagnetic induction, this change in magnetic flux induces an emf in the rod.

The direction of the induced emf will be such that it opposes the change in magnetic flux. As the rod falls, the magnetic flux through it increases. Therefore, the induced emf will be in a direction such that it generates a current that produces a magnetic field opposing the increase in magnetic flux.

Since the Earth's magnetic field lines generally run from north to south, and the rod is falling along the east-west direction, the induced emf will be in a direction such that it creates a current that generates a magnetic field opposing the Earth's magnetic field.

In summary, yes, there will be an emf induced at the ends of the metallic rod as it falls under gravity, and this induced emf will be in a direction such that it opposes the change in magnetic flux caused by the rod's motion.