Four particles $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D with masses $\mathrm{m}_{\mathrm{A}}=\mathrm{m}$, $\mathrm{m}_{\mathrm{B}}=2 \mathrm{~m}, \mathrm{~m}_{\mathrm{C}}=3 \mathrm{~m}$ and $\mathrm{m}_{\mathrm{D}}=4 \mathrm{~m}$ are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is :
Select the correct option:
A
Zero
B
$a(\hat{i}+\hat{j})$
C
$\frac{a}{5}(\hat{i}+\hat{j})$
D
$\frac{a}{5}(\hat{i}-\hat{j})$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$\begin{aligned} & a_{C M}=\frac{(2 m) a \hat{j}+3 m \times a \hat{i}+m a(-\hat{i})+4 m \times a(-\hat{j})}{2 m+3 m+4 m+m} \\ & =\frac{2 a \hat{i}-2 a \hat{j}}{10}=\frac{a}{5}(\hat{i}-\hat{j})\end{aligned}$
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