**Introduction:**

Genetic variability refers to the diversity in genetic makeup among individuals of a species. It is essential for the survival and adaptation of organisms to changing environments. Several factors contribute to genetic variability, including independent assortment, linkage, crossing over, and mutation. In this context, the question asks which of these factors is responsible for increasing genetic variability as the length of a chromosome increases.

**Explanation:**

The correct answer is option 'C', crossing over. Here's why:

**1. Independent Assortment:**
- Independent assortment occurs during meiosis when homologous chromosomes separate and are randomly distributed into gametes.
- It leads to genetic variability by creating different combinations of alleles from different genes.
- However, the length of a chromosome does not directly influence independent assortment. It is a random process that occurs during meiosis.

**2. Linkage:**
- Linkage refers to the phenomenon where genes located close to each other on the same chromosome tend to be inherited together.
- It reduces genetic variability because genes that are closely linked are less likely to undergo independent assortment.
- However, the length of a chromosome does not directly affect linkage. It depends on the distance between genes on the chromosome.

**3. Crossing Over:**
- Crossing over occurs during meiosis when homologous chromosomes exchange genetic material.
- It leads to genetic variability by creating new combinations of alleles within a chromosome.
- The longer the chromosome, the more opportunities there are for crossing over to occur.
- As a result, longer chromosomes have a higher chance of genetic recombination, leading to increased genetic variability.

**4. Mutation:**
- Mutation refers to changes in the DNA sequence of a gene.
- While mutation can introduce new variations in the genetic material, it is not directly influenced by the length of a chromosome.
- Mutations can occur in any region of the genome, regardless of the chromosome length.

**Conclusion:**

In summary, the correct answer to the question is option 'C', crossing over. The length of a chromosome influences genetic variability through the process of crossing over, which leads to the creation of new combinations of alleles within the chromosome. Independent assortment, linkage, and mutation are also important factors in generating genetic variability, but they are not directly affected by the length of a chromosome.