Name: Variable Mass System
Uploaded: 2019-07-19
Duration: 12 min 25 s
Description: In this video, we will look at how the laws of motion and their mathematical formulation apply to a variable mass system like a rocket. Don't miss it.

Question

Find the position of centre of mass of the uniform planner sheet shown in figure with respect to the origin $(O)$

Accepted Answer

For the given uniform planner sheet, we have to calculate the centre of mass. Given sheet is made of three square sheet of side length $a$ and negligible thickness. Consider the surface density of sheet is $σ kg m^{- 2}$ .

So, the mass of each square sheet of side $a$ can be written as $σ a^{2} kg$ .

Consider point $O$ as origin, the coordinate of the centre of mass of square $A$ is $(\frac{a}{2}, \frac{a}{2})$ , for square sheet $B$ is $(\frac{a}{2}, \frac{3 a}{2})$ and for square sheet $C$ is $(\frac{3 a}{2}, \frac{a}{2})$ .

The position of centre of mass along $x$ -axis can be written as,

$x_{cm} = \frac{m_{1} x_{1} + m_{2} x_{2} + \dots}{m_{1} + m_{2} + \dots}$

$x_{cm} = \frac{σ a^{2} \times \frac{a}{2} + σ a^{2} \times \frac{a}{2} + σ a^{2} \times \frac{3 a}{2}}{σ a^{2} + σ a^{2} + σ a^{2}} = \frac{5 a}{6}$

The position of centre of mass along $y$ -axis can be written as,

$y_{cm} = \frac{m_{1} y_{1} + m_{2} y_{2} + \dots}{m_{1} + m_{2} + \dots}$

$y_{cm} = \frac{σ a^{2} \times \frac{a}{2} + σ a^{2} \times \frac{3 a}{2} + σ a^{2} \times \frac{a}{2}}{σ a^{2} + σ a^{2} + σ a^{2}} = \frac{5 a}{6}$

So, the coordinate of the centre of mass of the given system will be at $(\frac{5 a}{6}, \frac{5 a}{6})$ .

Find the position of centre of mass of the uniform planner sheet shown in figure with respect to the origin $(O)$

Important Questions on Centre of Mass, Momentum and Collisions

Learn and Prepare for any exam you want !

Find the position of centre of mass of the uniform planner sheet shown in figure with respect to the origin (O)

Important Questions on Centre of Mass, Momentum and Collisions

Learn and Prepare for any exam you want !

Find the position of centre of mass of the uniform planner sheet shown in figure with respect to the origin $(O)$