Name: Linear Momentum of a System of Particles
Uploaded: 2019-07-19
Duration: 10 min 32 s
Description: Linear momentum is one of the most important concepts in physics. Watch this video to dive deep to visualise linear momentum of a system of particles.

Question

A disc of radius

R

is cut out from a larger disc of radius

2 R

in such a way that the edge of the hole touches the edge of the disc. Locate the centre of mass of the residual disc.

Accepted Answer

Let us consider the centre of the larger disc as the origin and the line joining the centres of the removed part and the larger disc as $x -$ axis.

As the remaining part is uniform and symmetric about $x -$ axis, its centre of mass must lie on the $x -$ axis only, due to symmetry.

Let us consider the position of the centre of mass of the remaining portion is $(x, 0) .$ Now, if we put back the removed portion, it becomes the complete large disk with centre at the origin.

Hence, the centre of mass of this combined system will be $(0, 0)$ .

So,

$0 = \frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}$ ,

where $m_{1}$ and $m_{2}$ are the masses of the remaining portion and the removed disc, respectively.

As the density and thickness is uniform,

$m \propto area$

$\Rightarrow \frac{m_{1}}{m_{2}} = \frac{(4 π R^{2} - π R^{2})}{π R^{2}} = \frac{3}{1}$

Considering the mass of the smaller disc as $m$ , we can write the mass of the remaining portion as $3 m$ .

And $2 R$

Thus, the position of the concentrated masses in the given system,

$0 = \frac{3 m \times x + m \times R}{3 m + m}$

$x = - \frac{R}{3}$ .

$∴$ Position of the centre of mass of the remaining section is opposite to the line joining both the centres at a distance $(\frac{R}{3})$ from the centre of the larger disc.

A disc of radius $R$ is cut out from a larger disc of radius $2 R$ in such a way that the edge of the hole touches the edge of the disc. Locate the centre of mass of the residual disc.

Important Questions on Centre of Mass, Linear Momentum, Collision

Learn and Prepare for any exam you want !

A disc of radius R is cut out from a larger disc of radius 2R in such a way that the edge of the hole touches the edge of the disc. Locate the centre of mass of the residual disc.

Important Questions on Centre of Mass, Linear Momentum, Collision

Learn and Prepare for any exam you want !

A disc of radius $R$ is cut out from a larger disc of radius $2 R$ in such a way that the edge of the hole touches the edge of the disc. Locate the centre of mass of the residual disc.