JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion

Three particles of masses \(50\, g\), \(100\, g\) and \(150\, g\) are placed at the vertices of an equilateral triangle of side \(1\, m\) (as shown in the figure). The \((x, y)\) coordinates of the centre of mass will be

A \(\left( {\frac{{\sqrt 3 }}{7}\,m,\,\frac{7}{{12}}\,m} \right)\)
B \(\left( {\frac{7}{{12}}m,\,\frac{{\sqrt 3 }}{8}\,m} \right)\)
C \(\left( {\frac{{\sqrt 3 }}{4}\,m,\,\frac{5}{{12}}\,m} \right)\)
D \(\left( {\frac{7}{{12}}m,\,\frac{{\sqrt 3 }}{4}\,m} \right)\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\left( {\frac{7}{{12}}m,\,\frac{{\sqrt 3 }}{4}\,m} \right)\)

Step-by-step Solution

Detailed explanation

The co-ordinates of the center of mass \({\overrightarrow r _{cm}} = \frac{{0 + 150 \times \left( {\frac{1}{2}i + \frac{{\sqrt 3 }}{2}\hat j} \right) + 100 \times \hat i}}{{300}}\) \({\overrightarrow r _{cm}} = \frac{7}{{12}}\hat i + \frac{{\sqrt 3 }}{4}\hat j\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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