A square plate and a circular plate made up of same material are placed touching each other on a horizontal table. If the side length of square plate is equal to diameter of the circular plate then the centre of mass of the system will be:

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inside the square plate.

inside the circular plate.

outside the system.

at the point of contact.

answer is A.

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Detailed Solution

If $σ$ be the surface density of mass of the square and circular plates , then

$m_{1}$ =Mass of the sqaure = $a^{2} σ$ .

$m_{2}$ = Mass of the circular plate = π $a^{2} σ$

$m_{1}$ > $m_{2}$

The square plate and the circular plate can be replaced by two particles of mass m1 and m2 respectively.

$r_{1}$ = Distance of COm from $m_{1}$ = $\frac{m_{2} a}{m_{1} + m_{2}}$

$r_{2}$ = Distance of COM from $m_{2}$ = $\frac{m_{1} a}{m_{1} + m_{2}}$

$r_{1}$ < $r_{2}$ and $r_{1}$ < $\frac{a}{2} .$

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