Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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A Circular Plate of Diameter D is Kept in Contact with a Square Plate of Edge D as Show in Figure. the Density of the Material and the Thickness Are Same Everywhere. - Physics


A circular plate of diameter d is kept in contact with a square plate of edge d as show in figure. The density of the material and the thickness are same everywhere. The centre of mass of the composite system will be 


  • inside the circular plate

  • inside the square plate

  • at the point of contact

  • outside the system.

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inside the square plate

Let m1 be the mass of circular plate and m2 be the mass of square plate. 
The thickness of both the plates is t.
\[\text{ mass = density ×  volume}\]
\[ m_1 = \rho\pi \left( \frac{d}{2} \right)^2 t \]
\[ m_2 = \rho d^2 t\]

Centre of mass of the circular plate lies at its centre.
Let the centre of circular plate be the origin.
\[\vec{r}_1 = 0\]
Centre of mass of the square plate lies at its centre.
\[\vec{r}_2 = 2d\]
\[\text{Now,} \]
\[R = \frac{m_1 \vec{r}_1 + m_2 \vec{r}_2}{m_1 + m_2}\]
\[ = \frac{m_1 \times 0 + \rho d^2 t \times 2d}{\rho\pi \left( \frac{d}{2} \right)^2 t + \rho d^2 t}\]
\[ = \frac{2d}{\frac{\pi}{4} + 1} = 1 . 12d\]
\[ \Rightarrow \text{R > d}\]
\[\therefore\] Centre of mass of the system lies in the square plate.

  Is there an error in this question or solution?
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HC Verma Class 11, 12 Concepts of Physics 1
Chapter 9 Centre of Mass, Linear Momentum, Collision
MCQ | Q 6 | Page 157
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