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

Three identical spheres, each of mass \(M ,\) are placed at the corners of a right angle triangle with mutually perpendicular sides equal to \(2 \;m\) (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of centre of mass.

A \(\frac{4}{3}(\hat{i}+\hat{j})\)
B \(2(\hat{i}+\hat{j})\)
C \((\hat{i}+\hat{j})\)
D \(\frac{2}{3}(\hat{i}+\hat{j})\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{2}{3}(\hat{i}+\hat{j})\)

Step-by-step Solution

Detailed explanation

\(x_{c m}=\frac{M \times 0+M \times 0+M \times 2}{3 M}=\frac{2}{3}\) \(y_{c m}=\frac{M \times 0+M \times 0+M \times 2}{3 M}=\frac{2}{3}\)

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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