KCET · Physics · Laws of Motion

A block of certain mass is placed on a rough inclined plane. The angle between the plane and the horizontal is \(30^{\circ}\). The coefficients of static and kinetic frictions between the block and the inclined plane are 0.6 and 0.5 respectively. Then, the magnitude of the acceleration of the block is [Take \(\left.g=10 \mathrm{~ms}^{-2}\right]\)

A \(2 \mathrm{~ms}^{-2}\)
B zero
C \(0.196 \mathrm{~ms}^{-2}\)
D \(0.67 \mathrm{~ms}^{-2}\)

Verified Solution

Answer & Solution

Correct Answer

(B) zero

Step-by-step Solution

Detailed explanation

From the diagram, frictional force
\(f_s=\mu R=\mu m g \cos 30^{\circ}\)
\(=0.6 \times m g \times \frac{\sqrt{3}}{2}\)
\(=0.3 \sqrt{3} \mathrm{mg}=0.5196 \mathrm{mg}\)
Magnitude of force pulling the block along the plane downward,
\(F^{\prime}=m g \sin 30^{\circ}=m g / 2=0.5 \mathrm{mg}\)
Since, \(\quad f_s \gt F^{\prime}\)
Hence, block will not move.
\(\therefore a=0\)

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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