The correct answer is: to.
The preposition “to” is used to indicate the purpose or goal of an action. In this case, the action is “contributes” and the goal is “the child’s mental development.”
The preposition “on” is used to indicate the effect of an action. In this case, the action is “contributes” and the effect is “the child’s mental development.”
The preposition “in” is used to indicate the location of an action. In this case, the action is “contributes” and the location is “the child’s mental development.”
The preposition “none of these” is not a correct answer because it does not indicate the purpose or goal of the action.