Question

State Lenz’s law.
A metallic rod held horizontally along east-west direction, is allowed to fall under gravity. will there be an $e.m.f$. Induced at its ends $?$ Justify your answer.

Answer 1

Hint The above statement is considered to decide the emf of a metallic rod. according to Lenz's law so that we can analyze the law of the Lenz concerning the statement is right. It also applies to the direction of the rod and the gravity of the earth.
Useful formula
Lenz’s law formula,
$ \in = - N\dfrac{{\partial \phi B}}{{\partial t}}$
$ \in $ is induced $emf$
$N$ is number of turns in coil
$\partial \phi B$ is change in magnetic flux
$\partial t$ is change in time

Complete step by step procedure
Given by,
A metallic rod held horizontally along east-west direction, is allowed to fall under gravity. will there be an $e.m.f$.
At the open ends of a closed loop, the polarity of the induced emf tends to create a current that opposes the magnetic Flux shift that generated it.

At the end, Emf will be induced. In a metal rod that freely falls under gravity, and thus, the magnetic flux changes.$emf$ is induced
In other words,
The law of Lenz states that the polarity of induced emf is such that it generates a current that opposes the change in its producing magnetic flux.
As the magnetic flux increases, EMF will be induced in the rod.
The magnetic flux changes when a metal rod held horizontally in the east-west direction is allowed to fall freely under gravity drop from north to south and the emf is induced in it.
Hence,

Yes, emf will be induced in the rod as there is change in magnetic flux.

Note When the path caused by emf is such that the reason generating it is opposed. We know that where the magnetic field is from north to south, the earth is magnetic as well. It thus acquires velocity when the conductor fails under gravity and therefore causes an e.m.f.