Answer
a. tips to the left
b. II is the best explanation
Work Step by Step
The location of the center of mass of a two-dimensional system of objects is defined as
$\displaystyle \mathrm{X}_{\mathrm{c}\mathrm{m}}=\frac{m_{1}x_{1}+m_{2}x_{2}+\cdots}{m_{1}+m_{2}+\cdots}=\frac{\sum mx}{M}\qquad$9-14
and
$\displaystyle \mathrm{Y}_{\mathrm{c}\mathrm{m}}=\frac{m_{1}\mathrm{y}_{1}+m_{2}y_{2}+\cdots}{m_{1}+m_{2}+\cdots}=\frac{\sum my}{M}\qquad$9-15
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a.
Let $m_{1}$ be the mass to the left of the fulcrum, and $m_{2}$ to the right.
$x_{1}$ is farther to the left of the fulcrum than $x_{2}$ is, because it has almost double the length of $m_{2}.$
Since $m_{1}=m_{2},$
$\displaystyle \mathrm{X}_{\mathrm{c}\mathrm{m}}=\frac{m(x_{1}+x_{2})}{2m}=\frac{x_{1}+x_{2}}{2},$
which will be left of the fulcrum, so the object will tip to the left.
b.
I is wrong. The sheet will be level if the center of mass is directly above it.
II is correct.
III is wrong for the same reason as I.