Question

A block of mass 2 kg is placed on a rough inclined plane at 30° to the horizontal. The coefficient of static friction is 0.4. Will the block slide down?

• A. Yes, with acceleration
• B. No, it remains at rest
• C. It depends on the value of kinetic friction
• D. It moves with constant velocity

Hint:

When analyzing motion on an incline, compare the component of gravitational force with the maximum static friction force to determine if the object will move.

Answer 1

The Correct Option is B

The forces acting on the block are:
1. The component of gravitational force along the incline, \( F_{\text{gravity}} = mg \sin \theta \)
2. The maximum static friction force, \( F_{\text{friction}} = \mu_s mg \cos \theta \) For the block to slide down, the component of gravitational force must overcome the friction force. \[ F_{\text{gravity}} = mg \sin \theta = 2 \times 9.8 \times \sin 30^\circ = 2 \times 9.8 \times 0.5 = 9.8 \, \text{N} \] \[ F_{\text{friction}} = \mu_s mg \cos \theta = 0.4 \times 2 \times 9.8 \times \cos 30^\circ = 0.4 \times 2 \times 9.8 \times 0.866 = 6.77 \, \text{N} \] Since the frictional force is greater than the component of gravity along the incline, the block does not slide.
Final answer
Answer: \(\boxed{\text{B}}\)