Explanation:

- Render: This option is indeed fitting. The phrase "render help" means to provide or give help, which is appropriate for the context of assisting the homeless and physically disabled people.

- Exert: Typically means to apply or put forth effort or force. It's not usually used with the word "help" in this context.

- Donate: Often relates to giving money, goods, or time. While relevant in terms of helping, it specifically implies giving something tangible.

- Contribute: Similar to donate but typically implies a group effort or adding towards a collective goal. It might not be the best fit for the direct act of giving help.

Your choice of "render" is indeed the most suitable.