Does the Gravitational Force at the Event Horizon Increase with Black Hole Mass?

[bowlbase]

Homework Statement

I got a problem wrong on a quiz and I'm pretty positive on all the other questions as being correct but maybe this one..

How does the gravitational force at the event horizon (Schwarzschild radius) behave as the black hole mass increases?

Homework Equations

The Attempt at a Solution

I assumed that by definition of the event horizon the force is constant no matter how the mass changes since the radius will move with it. Is this correct?

 

[gneill]

Start with the expression for the Schwarzschild radius. Compare with the expression for gravitational acceleration (I think the Newtonian version g = GM/r² will do for qualitative results). Can you create an expression gravitational acceleration at the Schwarzschild radius?