A $10$ cm $-$sided plastic cube floats submerged in a bath of heavy oil, secured to the bottom of the container by a string. The setup is such that $8$ cm of the cube is submerged in the oil. The plastic has a density of $0\mathrm{.}65\frac{g}{c}{m}^3,$ while the oil's density is $1\mathrm{.}75\frac{g}{c}{m}^3.$

What is the tension in the string?

$($A$)17\mathrm{.}15$ N

$6\mathrm{.}37$ N

&$.7\mathrm{.}35$ N

$10\mathrm{.}78$ N

$13\mathrm{.}72$ N

$(10$ points$)$

$T=W+F_B$

$T=mg+p_{fI}{V}_{a}g$

$T=1\mathrm{.}53+(1\mathrm{.}75)({10}^3)(9\mathrm{.}8)$

Pftrolisp $9=17151\mathrm{.}5317\mathrm{.}15N$

$w_{\text{a}\text{b}\text{e}}=p_{\text{c}\text{u}\text{b}\text{e}}vvg$

$P_{\text{c}\text{u}\text{b}}=0\mathrm{.}8p_{\text{c}\text{i}\text{l}}1\mathrm{.}4+0\mathrm{.}2p_{\text{p}\text{l}\text{a}\text{s}\text{t}\text{i}\text{c}}$

$=1\mathrm{.}53$

A small fishing boat can be approximate