Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
Advertisement Remove all ads

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

MCQ

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 

Options

  • inside the circular plate

  • inside the square plate

  • at the point of contact

  • outside the system.

Advertisement Remove all ads

Solution

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?
Advertisement Remove all ads

APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 9 Centre of Mass, Linear Momentum, Collision
MCQ | Q 6 | Page 157
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×