A force F1→ of magnitude 4 N acts on an object of mass 1 kg at origin in a direction 30° above the positive x- axis. A second force F2→ of magnitude 4 N acts on the same object in the direction of the positive y- axis. The magnitude of the acceleration of the object is nearly

AP EAMCET · PHYSICS · Mathematics in Physics

A force $\vec{F_{1}}$ of magnitude $4 N$ acts on an object of mass $1 kg$ at origin in a direction $30 °$ above the positive $x$ - axis. A second force $\vec{F_{2}}$ of magnitude $4 N$ acts on the same object in the direction of the positive $y$ - axis. The magnitude of the acceleration of the object is nearly

A $6.9 m s^{- 2}$
B $7.6 m s^{- 2}$
C $4.3 m s^{- 2}$
D $8.0 m s^{- 2}$

Verified Solution

Answer & Solution

Correct Answer

(A) $6.9 m s^{- 2}$

Step-by-step Solution

Detailed explanation

Using parallelogram law of vector addition, Resultant force acting on object is FR=F12+F22+2F1F2cosθ, here, θ=90°-30°=60° is angle between the forces. Putting the values, we have FR=42+42+244cos60°=6.9 N Acceleration of the object is…

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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