Explanation:
To determine whether a block placed on a rough inclined plane of inclination 30 degrees can be pushed upwards, we need to consider the forces acting on the block and analyze the conditions required for it to move in the desired direction.

Forces acting on the block:
1. Weight (W): The gravitational force acting vertically downwards.
2. Normal force (N): The force exerted by the inclined plane perpendicular to it.
3. Friction force (f): The force opposing the motion and parallel to the inclined plane.

Conditions for pushing the block upwards:
In order to push the block upwards, we need to overcome the forces that oppose its motion. These forces include the weight of the block and the friction force acting parallel to the inclined plane.

1. Weight: The weight of the block can be broken down into two components: the perpendicular component (W⊥) and the parallel component (W‖) to the inclined plane.
- W⊥ = W * cos(30°) = W * √(3)/2
- W‖ = W * sin(30°) = W * 1/2

2. Friction force: The friction force (f) opposes the motion and can be calculated using the equation f = μN, where μ is the coefficient of friction between the block and the inclined plane, and N is the normal force.
- N = W⊥ = W * √(3)/2
- f = μ * N = μ * W * √(3)/2

Condition for equilibrium:
For the block to be in equilibrium while being pushed upwards, the force applied must be greater than or equal to the opposing forces (weight and friction force). Mathematically, we can express this as:
- F ≥ W‖ + f

Conclusion:
If the applied force (F) is greater than or equal to the sum of the parallel component of weight (W‖) and the friction force (f), the block can be pushed upwards on the rough inclined plane of inclination 30 degrees. However, if the applied force is less than the sum of these forces, the block will not move upwards and will remain stationary or slide downwards.

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