A boy of mass 40 kg climbs up a rope with an acceleration of `2 ms^(-2)` . What is the tension in the rope ?

Options

A. 472 N
B. 435 N
C. 232 N
D. 568 N

Answer

To solve the problem of finding the tension in the rope when a boy of mass 40 kg climbs up with an acceleration of 2 m/s², we can follow these steps:

### Step 1: Identify the Forces Acting on the Boy
When the boy climbs up, two main forces act on him:
1. The gravitational force (weight) acting downward, which is given by \( W = mg \).
2. The tension \( T \) in the rope acting upward.

### Step 2: Write Down the Known Values
- Mass of the boy, \( m = 40 \, \text{kg} \)
- Acceleration of the boy, \( a = 2 \, \text{m/s}^2 \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)

### Step 3: Set Up the Equation of Motion
Since the boy is climbing up with an acceleration, we can apply Newton's second law. The net force acting on the boy can be expressed as:
\[ T - mg = ma \]
Where:
- \( T \) is the tension in the rope,
- \( mg \) is the weight of the boy,
- \( ma \) is the net force due to the upward acceleration.

### Step 4: Rearrange the Equation to Solve for Tension
Rearranging the equation gives us:
\[ T = mg + ma \]

### Step 5: Substitute the Known Values
Now we can substitute the known values into the equation:
\[ T = m(g + a) \]
\[ T = 40 \, \text{kg} \times (9.8 \, \text{m/s}^2 + 2 \, \text{m/s}^2) \]
\[ T = 40 \, \text{kg} \times 11.8 \, \text{m/s}^2 \]

### Step 6: Calculate the Tension
Now we perform the multiplication:
\[ T = 40 \times 11.8 = 472 \, \text{N} \]

### Conclusion
The tension in the rope is \( 472 \, \text{N} \).

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