A lift of mass 100 kg is moving upwards with an acceleration of 1 `m//s^(2)`. The tension developed in the string, which is connected to lift is (`g=9.8m//s^(2)`)

Options

A. 980 N
B. 1080 N
C. 1100 N
D. 1000 N

Answer

To find the tension in the string connected to the lift, we can use Newton's second law of motion. The forces acting on the lift are the tension in the string (T) and the weight of the lift (W).

### Step-by-step solution:

1. **Identify the forces acting on the lift**:
- The weight of the lift (W) is given by the formula:
\[ W = m \cdot g \]
where \( m = 100 \, \text{kg} \) (mass of the lift) and \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity).

2. **Calculate the weight of the lift**:
\[ W = 100 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 980 \, \text{N} \]

3. **Apply Newton's second law**:
According to Newton's second law, the net force (F_net) acting on the lift can be expressed as:
\[ F_{\text{net}} = T - W \]
Since the lift is accelerating upwards, we can also express the net force as:
\[ F_{\text{net}} = m \cdot a \]
where \( a = 1 \, \text{m/s}^2 \) (upward acceleration of the lift).

4. **Set the equations equal**:
Combining the two expressions for net force, we have:
\[ T - W = m \cdot a \]

5. **Substitute known values**:
Substituting the values we calculated:
\[ T - 980 \, \text{N} = 100 \, \text{kg} \cdot 1 \, \text{m/s}^2 \]
\[ T - 980 \, \text{N} = 100 \, \text{N} \]

6. **Solve for tension (T)**:
Rearranging the equation to solve for T:
\[ T = 980 \, \text{N} + 100 \, \text{N} \]
\[ T = 1080 \, \text{N} \]

### Final Answer:
The tension developed in the string is **1080 N**.