1. The compound with formula $(C_7H_5O_2)_2$ is benzoyl peroxide.

   Its structure is: $C_6H_5CO-O-OCOC_6H_5$

2. On exposure to light $(h\nu)$, the weak peroxide bond $O-O$ undergoes homolytic cleavage.

   So the first intermediate formed is: $C_6H_5COO\cdot$ This is called the benzoyloxy radical.

   The cleavage step is: $C_6H_5CO-O-OCOC_6H_5 \xrightarrow{h\nu} 2\,C_6H_5COO\cdot$

3. The benzoyloxy radical is unstable and undergoes decarboxylation: $C_6H_5COO\cdot \rightarrow C_6H_5\cdot + CO_2$

4. Since two benzoyloxy radicals are formed, overall: $2\,C_6H_5COO\cdot \rightarrow 2\,C_6H_5\cdot + 2CO_2$

5. Therefore, the intermediate $X$ is: $X = 2\,C_6H_5COO\cdot$ i.e. the benzoyloxy radical.

6. Hence the correct option is the one corresponding to benzoyloxy radical.

Since the stored correct answer is D, and this matches the expected intermediate, I agree with the stored answer.