Grounding/earthing in a simple circuit

[Dessert]

I know that the purpose of grounding is to set a potential reference or to set up a sink for charges. In the circuit in the attachment, what is the function of the grounding? Does it affect the voltage drop across the two resistors?

Assume that the connection wire has no resistance and the battery has no internal resistance.

 

[Stonebridge]

No it doesn't affect the voltage drop (pd) across the two resistors.
What it does do is to set the potential of the point between the two resistors at zero.
To the left of the left R the potential will be positive and to the right of the right R the potential will be negative.

 

[Dessert]

if the emf of the battery is 1V, does it mean that the potential of the circuit is 0.5V maximum, and then drop to 0V at the grounding point, and then to -0.5V after the current passes through the second R?

 

[Stonebridge]

Yes. The potential of the left side of the circuit will be +0.5V and the potential of the right side of the circuit will be -0.5V
This gives a potential difference of 0.5V - (-0.5V) = 1V