In recent years, the problem of rumours on online social media (OSM) has attracted lots of attention. Researchers have started investigating from two main directions. First is the descriptive analysis of rumours and secondly, proposing techniques to detect (or classify) rumours. In the descriptive line of works, where researchers have tried to analyse rumours using NLP approaches, there isnt much emphasis on psycho-linguistics analyses of social media text. These kinds of analyses on rumour case studies are vital for drawing meaningful conclusions to mitigate misinformation. For our analysis, we explored the PHEME9 rumour dataset (consisting of 9 events), including source tweets (both rumour and non-rumour categories) and response tweets. We compared the rumour and nonrumour source tweets and then their corresponding reply (response) tweets to understand how they differ linguistically for every incident. Furthermore, we also evaluated if these features can be used for classifying rumour vs. non-rumour tweets through machine learning models. To this end, we employed various classical and ensemble-based approaches. To filter out the highly discriminative psycholinguistic features, we explored the SHAP AI Explainability tool. To summarise, this research contributes by performing an in-depth psycholinguistic analysis of rumours related to various kinds of events.