pls try this ques anybody..!!!
Answers
Solution;-
If that small circle doesn't taken out,then,
Xcm about O=
Note:-(-) sign denotes the left of O
{hope it helps you}
that small circle doesn't taken out,then,
Xcm about O=
\begin{lgathered}\frac{mass \: of \: cicle \times distance \: of \: centre \: of \: circle \: from \: o + mass \: of \: square \times 0}{mass \: of \: circle \: + mass \: of \: square} \\ clearly \: distance \: of \: centre \: of \: circle \\ from \: o = 4 + 2 = 6cm \\ let \: th \: mass \: per \: unit \: area \: of \: square \: and \\ circlee \: \: be \: p \\ then \: mass \: of \: circle = p \times \pi \times 16 \\ mass \: of \: square = 400 \times p \\ puttiing \: this \: value \: we \: get \\ centre \: of \: mass \: if \:circle \: is \: not \: taken \: out \\ = \frac{0 + p \times 96\pi}{16\pi \times p + 400 \times p } \\ = \frac{16\pi}{16\pi + 400} \\ but \: as \: the \: mass \: of \: circle \: is \: taken \: out \: so \\ to \: get \: the \: centre \: of \: mass \: of \: remaining \: part \\ take \: the \: mass \: of \: circle \: as \: negative \\ required \: centre \: of \: mass \\ = \frac{ - 96\pi}{400 - 16\pi} = - . 73 \\ so \: centre \: of \: mass \: will \:be \: on \: .73 \: left \: of \: o\end{lgathered}
massofcircle+massofsquare
massofcicle×distanceofcentreofcirclefromo+massofsquare×0
clearlydistanceofcentreofcircle
fromo=4+2=6cm
letthmassperunitareaofsquareand
circleebep
thenmassofcircle=p×π×16
massofsquare=400×p
puttiingthisvalueweget
centreofmassifcircleisnottakenout
=
16π×p+400×p
0+p×96π
=
16π+400
16π
butasthemassofcircleistakenoutso
togetthecentreofmassofremainingpart
takethemassofcircleasnegative
requiredcentreofmass
=
400−16π
−96π
=−.73