23P1Q05

5          B

Method 1

The overall C.G. lies somewhere between the C.G. of the top half and the bottom half.

Since the top half has twice the mass as the bottom half, the resultant C.G. should lie twice as near C.G. of the top half as the bottom. Meaning the C.G. is \displaystyle \frac{1}{3}\times 4\text{ cm}and \displaystyle \frac{2}{3}\times 4\text{ cm}from the C.G. of the top and bottom halves respectively.

From P, the distance would be \displaystyle 2+\frac{2}{3}(4)=4.7\text{ cm}

Method 2

Let the mass of the top half be 2m so the bottom half would be m.

Let the distance between the C.G. and P be x.

\displaystyle \begin{aligned}  & 2m\times 6.0+m\times 2.0=3m\times x \\ & x=4.67\text{ cm} \end{aligned}

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