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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीThree particles of masses \( 100\text{ g} \), \( 150\text{ g} \), and \( 200\text{ g} \) are placed at the vertices \( O(0,0) \), \( A(0.5\text{ m}, 0) \), and \( B(0.25\text{ m}, 0.25\sqrt{3}\text{ m}) \) of an equilateral triangle respectively. If an additional fourth mass of \( 450\text{ g} \) is placed at a point \( D \) such that the centre of mass of the four-particle system shifts to the origin \( (0,0) \), what are the coordinates of point \( D \)?
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Correct answer · Option A
\( (-\frac{5}{18}\text{ m}, -\frac{1}{3\sqrt{3}}\text{ m}) \)
Explanation
For the first three masses totaling \( 450\text{ g} \), \( X_{\text{cm1}} = \frac{5}{18}\text{ m} \) and \( Y_{\text{cm1}} = \frac{1}{3\sqrt{3}}\text{ m} \). For total CM at \( (0,0) \), \( m_4 \vec{r}_4 + m_{123} \vec{r}_{\text{cm1}} = 0 \implies 450 \vec{r}_4 = -450 \vec{r}_{\text{cm1}} \implies \vec{r}_4 = -\vec{r}_{\text{cm1}} = (-\frac{5}{18}\text{ m}, -\frac{1}{3\sqrt{3}}\text{ m}) \).
