# Homework Help: Cylinder with hole in it

1. Dec 24, 2013

### physicsboy121

1. The problem statement, all variables and given/known data
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?

2. Relevant 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?

3. The attempt at a solution
Torque_net = (6.5)(distance of center of mass from cylinder's center) - (F)(R)=0

2. Dec 24, 2013

### haruspex

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

3. Dec 24, 2013

### 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 xcom in terms of R.
Also g shall be involved in the torque calculation..

4. Dec 25, 2013

### physicsboy121

I got it, thanks so much!