Test Index

Center of Mass

Section: Physics

Question : 3 of 18

Marks: +1, -0

Solution:

σ

be the mass per unit area, Then,

\sigma\;=\;\frac{3}{2\times 1+1\times 1}

\;=1 \text{ kg}/\text{m}^2

∴ mass of rectangle-1,

m_1=\sigma A_1=1 \times 2 \times 1=2 \text{ kg}

mass of rectangle-2,

\;m_2=\sigma A_2=1 \times 1 \times 1=1 \text{ kg}

\; \therefore X_{CM}=\;\frac{m_1 x_1+m_2 x_2}{m_1+m_2}

\; \;\; =\;\frac{2 \times \frac{1}{2}+1 \times \frac{3}{2}}{2+1}=\;\frac{5}{6} \text{ m}

and

Y_{ CM }=\;\frac{m_1 y_1+m_2 y_2}{m_1+m_2}

=\;\frac{2 \times 1+1 \times \frac{1}{2}}{2+1}=\;\frac{5}{6} \text{ m}

∴ Centre of mass

= (X_{CM}, Y_{CM}) = \left(\;\frac{5}{6} \text{ m}, \;\frac{5}{6} \text{ m}\right)

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