TS EAMCET · Physics · Laws of Motion

A block of mass \(3 \mathrm{~kg}\) is pressed against a vertical wall by applying a force \(F\) at an angle \(30^{\circ}\) to the horizontal as shown in the figure. As a result, the block is prevented from falling down. If the coefficient of static friction between the block and wall is \(\sqrt{3}\), then the value of \(F\) is (use, \(g=10 \mathrm{~m} / \mathrm{s}^2\) )

A \(30 \mathrm{~N}\)
B \(15 \sqrt{3} \mathrm{~N}\)
C \(60 \sqrt{3} \mathrm{~N}\)
D \(60 \mathrm{~N}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(30 \mathrm{~N}\)

Step-by-step Solution

Detailed explanation

The given situation is shown below Normal reaction is \(\mathbf{N}=F \cos \theta=F \cos 30^{\circ}\) Friction force when block is just on the verge of sliding is \(f=\mu N=\mu F \cos 30^{\circ}=\frac{3}{2} F \quad[\therefore \mu=\sqrt{3}]\) As block is in equilibrium, friction=…

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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