COMEDK · Physics · 5. Laws of Motion

The resultant of two forces acting at an angle of \(120^{\circ}\) is \(10 \mathrm{~kg}-\mathrm{W}\) and is perpendicular to one of the forces. That force is

A \(\dfrac{10}{\sqrt{3}} \mathrm{~kg}-\mathrm{W}\)
B \(10 \mathrm{~kg}-\mathrm{W}\)
C \(20 \sqrt{3} \mathrm{~kg}-\mathrm{W}\)
D \(10 \sqrt{3} \mathrm{~kg}-\mathrm{W}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\dfrac{10}{\sqrt{3}} \mathrm{~kg}-\mathrm{W}\)

Step-by-step Solution

Detailed explanation

Let the two forces be \(F_1\) and \(F_2\). The angle between them is \(\theta = 120^{\circ}\). The resultant \(R = 10 \text{ kg-W}\) is perpendicular to \(F_1\). The formula for the angle \(\alpha\) that the resultant makes with \(F_1\) is given by…

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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