Center of gravity of an irregular object of mass

[Superfluous]

The center of gravity of an irregular object of mass 4.50 g is shown in the figure. You need to move the center of gravity 2.00 cm to the left by gluing on a tiny 1.60-g mass, which will then be considered as part of the object. Where should you attach this additional mass? Express your answer in cm to the left of the original center of gravity.

Well, to tell the truth, I don't know how to go about solving this at all. My physics instructor skipped over the section that included this, but still assigned the homework. The chapter that this problem is in includes a bunch of rigid-body equilibrium problems, which I have been solving by using Newton's laws and summing up torques, but this problem has really thrown me for a loop. Would someone please describe the process I use to solve this type of problem, or the relevant equations even?

Thanks.

 

[TVP45]

The center of gravity of an irregular object of mass 4.50 g is shown in the figure. You need to move the center of gravity 2.00 cm to the left by gluing on a tiny 1.60-g mass, which will then be considered as part of the object. Where should you attach this additional mass? Express your answer in cm to the left of the original center of gravity.

Well, to tell the truth, I don't know how to go about solving this at all. My physics instructor skipped over the section that included this, but still assigned the homework. The chapter that this problem is in includes a bunch of rigid-body equilibrium problems, which I have been solving by using Newton's laws and summing up torques, but this problem has really thrown me for a loop. Would someone please describe the process I use to solve this type of problem, or the relevant equations even?

Thanks.

Can you think of anything unique or special about the CG?

 

[Superfluous]

No, unforunately I do not understand what you're trying to point me towards.

 

[D H]

What is the relevant equation here -- the equation for the center of mass of a set of objects?

 

[Superfluous]

I am happy to report that I figured it out. I guess taking a break for awhile and coming back to it can do wonders. I re-read the section and took a stab at it:

\frac{m_{1}(0)+m_{2}(x)}{m_{1}+m_{2}}=2

Solved for x:

x=\frac{2(m_{1}+m_{2})}{m_{2}}

Plugged in values... got a result of about 7.63 cm. Seemed reasonable, so I tried it. Turned out to be correct. Thanks to everyone who tried to help.