If Young’s modulus for a material is zero, then the state of material should be

The correct option is Solid but powder.

To understand why, let us examine the definition of Young's modulus. Young's modulus ($Y$) is a measure of the ability of a material to withstand changes in length when under lengthwise tension or compression. It is defined as the ratio of longitudinal stress ($\sigma$) to longitudinal strain ($\epsilon$):
$Y=\frac{\sigma }{\epsilon }$

For a material to have a non-zero Young's modulus, it must be capable of sustaining a tensile or compressive stress that results in a proportional elastic strain. Let us analyze the states of matter given in the options:
1. Solid: Standard bulk solids have a definite shape and size. They offer resistance to deforming forces, giving them a well-defined, non-zero Young's modulus.
2. Gas: Gases do not have a fixed shape or volume and cannot support shear or longitudinal tensile stress under ordinary conditions; their resistance to compression is characterized by the bulk modulus, not Young's modulus.
3. Solid but powder: A powdered solid consists of minute, discrete solid particles. While individual particles are solid and have their own elasticity, the bulk powdered material as a whole cannot sustain a tensile stress (pulling force) or support longitudinal loads without flowing or shifting. Since any attempt to apply tensile stress to a pile of powder results in separation of particles with virtually zero resisting force, the longitudinal stress $\sigma \approx 0$ for a finite strain, leading to an effective bulk Young's modulus of zero.

Therefore, if Young's modulus for a material is zero, the state of the material should be solid but powder.