How Much Force is Needed to Keep a Drilled Cylinder at Rest?

[physicsboy121]

Homework Statement

A uniform cylinder of radius R and mass 8kg has an off-axis hole drilled through it at 2R/5. Its new mass is 6.5kg. The hole and cylinder are parallel with their centers being the same height. What horizontal force, F, must be applied on the top to keep the cylinder at rest?

Homework Equations

I tried writing a torque equation for static equilibrium. However, I need to know the center of mass for the cylinder with the drilled hole, but I do not know it. Is there a better approach to this problem?

The Attempt at a Solution

Torque_net = (6.5)(distance of center of mass from cylinder's center) - (F)(R)=0

 

[haruspex]

Just think it is a solid cylinder plus a thin cylinder of negative mass.

 

[kastelian]

Or you can imagine another hole, drilled symmetrically to the first, with the same mass taken out. The remaining cylinder will have 5 kg at x=0, one hole is actually filled with mass 1.5 kg at 2R/5. Then it shall be easy to calculate new x_com in terms of R.
Also g shall be involved in the torque calculation..

 

[physicsboy121]

I got it, thanks so much!