A light rope is passed over a pulley such that at its one end a block is attached , and on the other end a boy is climbing up with acceleration `g/2` relative to rope. Mass of the block is 30 kg and that of the boy is 40 kg. Find the tension and acceleration of the rope .

Explanation

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

### Step 1: Define Variables
Let:
- \( m_b = 40 \, \text{kg} \) (mass of the boy)
- \( m_{block} = 30 \, \text{kg} \) (mass of the block)
- \( g \) = acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \))
- \( a_1 \) = acceleration of the block (downward)
...