AP EAMCET · PHYSICS · Laws of Motion

When a body is placed on a rough plane (coefficient of friction $= μ$ ) inclined at an angle $θ$ to the horizontal, its acceleration is (acceleration due to gravity $= g$ )

A $g (\sin θ - μ \cos θ)$
B $g (\sin θ - \cos θ)$
C $g μ (\sin θ - \cos θ)$
D $g (μ \sin θ - \cos θ)$

Verified Solution

Answer & Solution

Correct Answer

(A) $g (\sin θ - μ \cos θ)$

Step-by-step Solution

Detailed explanation

Here is the diagram of the given situation, Friction will be acting in the direction opposite to the tendency of relative motion, f=μN=μmgcosθ Writing the force balance equations,…

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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When a body is placed on a rough plane (coefficient of friction=μ) inclined at an angle θ to the horizontal, its acceleration is (acceleration due to gravity =g)

Step-by-step Solution

When a body is placed on a rough plane (coefficient of friction $= μ$ ) inclined at an angle $θ$ to the horizontal, its acceleration is (acceleration due to gravity $= g$ )