A block rests on a fixed rough inclined plane and a horizontal force F is applied to it, as shown in the figure. Which of the following statements are correct? (1) Normal reaction on the block is F sin ⁡ θ + m g cos ⁡ θ (2) The frictional force is zero when F cos ⁡ θ = m g sin ⁡ θ (3) The value of limiting friction is μ ( m g sin ⁡ θ + F cos ⁡ θ ) (4) The value of limiting friction is μ ( m g sin ⁡ θ - F cos ⁡ θ )

Question

A block rests on a fixed rough inclined plane and a horizontal force F is applied to it, as shown in the figure. Which of the following statements are correct? (1) Normal reaction on the block is F sin ⁡ θ + m g cos ⁡ θ (2) The frictional force is zero when F cos ⁡ θ = m g sin ⁡ θ (3) The value of limiting friction is μ ( m g sin ⁡ θ + F cos ⁡ θ ) (4) The value of limiting friction is μ ( m g sin ⁡ θ - F cos ⁡ θ ), 1, 2, 3, 4, 2, 4, 2, 3

MARKS App · Accepted Answer

As the object is at rest, therefore from FBD, Normal Reaction N = m g cos ⁡ θ + F sin ⁡ θ .....(i) Limiting Friction f L = μ N = μ m g cos ⁡ θ + F sin ⁡ θ ......(ii) Also, if m g sin ⁡ θ = F cos ⁡ θ then the object has no tendency of motion; hence friction is zero in this case.

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