Three point masses M1-1-6 kg- M2-2-4 kg and M3-2 kg are placed at the corners of a thin massless rectangular sheet 1 -2 m- 1-0 m as shown in the figure below- Centre of mass of the system will be located at a point assuming M1 to be at the origin

Given, [ x_1 = 0 m amp; y_1 = 0 m amp; m_1 = 1.6 kg; x_2 = 0 m amp; y_2 = 1 nbsp; m amp; m_2 = 2.4 ...

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Byju's Answer

Standard XI

Physics

Intuition for COM

Three point m...

Question

Three point masses $M_{1} = 1.6 kg, M_{2} = 2.4 kg$ and $M_{3} = 2 kg$ are placed at the corners of a thin massless rectangular sheet $(1 .2 m \times 1.0 m)$ as shown in the figure below. Centre of mass of the system will be located at a point (assuming $M_{1}$ to be at the origin)

(0.8, 0.6) m

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(0.6, 0.8) m

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(0.4, 0.4) m

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(0.5, 0.6) m

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Solution

The correct option is C $(0.4, 0.4) m$
Given,
$\begin{matrix} x_{1} = 0 m & y_{1} = 0 m & m_{1} = 1.6 kg x_{2} = 0 m & y_{2} = 1 m & m_{2} = 2.4 kg x_{3} = 1.2 m & y_{3} = 0 m & m_{3} = 2.0 kg \end{matrix}$

$x_{cm} = \frac{m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3}}{m_{1} + m_{2} + m_{3}}$
$= \frac{1.6 * 0 + 2.4 * 0 + 2 (1.2)}{1.6 + 2.4 + 2} = 0.4 m$
$y_{cm} = \frac{m_{1} y_{1} + m_{2} y_{2} + m_{3} y_{3}}{m_{1} + m_{2} + m_{3}}$
$= \frac{1.6 * 0 + 2.4 * 1 + 2 (0)}{1.6 + 2.4 + 2} = 0.4 m$
$\Rightarrow (x_{cm}, y_{cm}) = (0.4, 0.4) m$

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Three point masses M1=1.6 kg,M2=2.4 kg and M3=2 kg are placed at the corners of a thin massless rectangular sheet (1.2 m×1.0 m) as shown in the figure below. Centre of mass of the system will be located at a point (assuming M1 to be at the origin)

The correct option is C ( 0.4,0.4 )mGiven, x1=0 my1=0 mm1=1.6 kgx2=0 my2=1 mm2=2.4 kgx3=1.2 my3=0 mm3=2.0 kg xcm=m1x1+m2x2+m3x3m1+m2+m3 =1.6∗0+2.4∗0+2(1.2)1.6+2.4+2=0.4 m ycm=m1y1+m2y2+m3y3m1+m2+m3 =1.6∗0+2.4∗1+2(0)1.6+2.4+2=0.4 m ⇒(xcm,ycm)=( 0.4,0.4 )m

Three point masses $M_{1} = 1.6 kg, M_{2} = 2.4 kg$ and $M_{3} = 2 kg$ are placed at the corners of a thin massless rectangular sheet $(1 .2 m \times 1.0 m)$ as shown in the figure below. Centre of mass of the system will be located at a point (assuming $M_{1}$ to be at the origin)