Question

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 a square plate is equal to the diameter of the circular plate then the centre of mass of the system will be

Answer 1

Answer:

Inside the square plate

Explanation:

The center of mass lies closer to the heavier mass. The square plate has more mass(it's side is equal to diameter of circle who's mass will be calculated using radius which will be half of the side of square).

Answer 2

The centre of the mass lies inside of the square plate.

Let the side length of the square plate and the diameter of the circular plate be x.

As both are made of the same material, the mass of each plate will be proportional to its area.

Hence the area of the square plate is $a^2$.

The area of the circular plate is $\frac{\pi a^2}{4}$.

We will assume the point where they touch as the origin.

The centre of mass of the square plate is at $\frac{-a}{2}$.

The centre of mass of the circular plate is at $\frac{a}{2}$.

Hence the centre of mass is

$\frac{-a^2*\frac{a}{2} +\frac{\pi a^2}{4} *\frac{a}{2} }{a^2+\frac{\pi a^2}{4} } = -0.06a$

The centre of mass is at -0.06a.

#SPJ3