Two blocks of mass 2 kg and 5 kg are connected by an ideal string passing over a pulley. The block of mass 2 kg is free to slide on a surface inclined at an angle of `30^@` with the horizontal whereas 5 kg block hangs freely. Find the acceleration of the system and the tension in the string.

Explanation

To solve the problem, we need to analyze the forces acting on both blocks and apply Newton's second law of motion. Let's break down the solution step by step.

### Step 1: Identify the forces acting on each block

1. **For the 2 kg block on the incline (Block 1)**:
- Weight (mg) acting downwards: \( W_1 = m_1 g = 2 \, \text{kg} \times 10 \, \text{m/s}^2 = 20 \, \text{N} \)
- The component of weight acting parallel to the incline: \( W_{1\parallel} = W_1 \sin(30^\circ) = 20 \sin(30^\circ) = 20 \times \frac{1}{2} = 10 \, \text{N} \)
- The component of weight acting perpendicular to the incline: \( W_{1\perpendicular} = W_1 \cos(30^\circ) = 20 \cos(30^\circ) = 20 \times \frac{\sqrt{3}}{2} = 10\sqrt{3} \, \text{N} \)
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