Mark the wrong statement

The correct answer is: "It is difficult to twist a long rod as compared to small rod".

Let us analyze each statement to understand why this is the incorrect (wrong) statement among the choices:

1. Sliding of molecular layer is much easier than compression or expansion:
When a material undergoes shearing stress, the molecular layers slide over one another. This shape deformation does not change the volume, which requires overcoming intermolecular repulsive or attractive forces to a much smaller degree than changing the volume (compression or expansion). Therefore, the shear modulus (associated with sliding/shearing) is generally much smaller than the bulk modulus (associated with compression/expansion), making sliding much easier. This statement is correct.

2. Reciprocal of bulk modulus of elasticity is called compressibility:
By definition, compressibility is the measure of the relative volume change of a fluid or solid as a response to a pressure change. Mathematically, compressibility ($C$) is the reciprocal of the bulk modulus ($B$):
$C=\frac{1}{B}$
This statement is correct.

3. It is difficult to twist a long rod as compared to small rod:
The restoring torque ($\tau$) required to produce an angle of twist $\theta$ in a cylinder/rod of length $l$, radius $r$, and shear modulus $\eta$ is given by the relation:
$\tau =\frac{\pi \eta r^4\theta }{2l}$
From this formula, we can see that the torque required to twist a rod by a certain angle $\theta$ is inversely proportional to its length ($l$):
$\tau \propto \frac{1}{l}$
This means that for a longer rod (larger $l$), the torque required to produce the same angle of twist is smaller. In other words, it is actually easier to twist a long rod than a short (small) rod of the same material and radius. Thus, the statement "It is difficult to twist a long rod as compared to small rod" is wrong.

4. Hollow shaft is much stronger than a solid rod of same length and same mass:
For a given mass and length, a hollow shaft has a larger radius than a solid shaft. Since the torque required to twist a cylinder scales with the fourth power of the radius ($r^4$), distributing the mass further from the axis of rotation significantly increases its torsional rigidity. Hence, a hollow shaft is much stronger (can resist more twisting torque) than a solid rod of the same mass and length. This statement is correct.