A lift of mass `1000kg` is moving with an acceleration of `1m//s^(2)` in upward direction. Tension developed in the string, which is connected to the lift, is.

Options

A. 9800 N
B. 10,800 N
C. 11,000 N
D. 10,000 N

Answer

To find the tension developed in the string connected to a lift moving upwards with an acceleration, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the lift (m) = 1000 kg
- Acceleration of the lift (a) = 1 m/s²
- Acceleration due to gravity (g) = 10 m/s² (approximately)

2. **Understand the Forces Acting on the Lift:**
- The forces acting on the lift are:
- Weight of the lift (downward): \( W = m \cdot g \)
- Tension in the string (upward): \( T \)
- Pseudo force (downward) due to the upward acceleration of the lift: \( F_{pseudo} = m \cdot a \)

3. **Calculate the Weight of the Lift:**
\[ W = m \cdot g = 1000 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 10000 \, \text{N} \]

4. **Calculate the Pseudo Force:**
\[ F_{pseudo} = m \cdot a = 1000 \, \text{kg} \cdot 1 \, \text{m/s}^2 = 1000 \, \text{N} \]

5. **Apply Newton's Second Law:**
When considering the forces acting on the lift, we can write the equation for tension:
\[ T - W - F_{pseudo} = 0 \]
Rearranging gives:
\[ T = W + F_{pseudo} \]

6. **Substitute the Values:**
\[ T = 10000 \, \text{N} + 1000 \, \text{N} = 11000 \, \text{N} \]

7. **Final Answer:**
The tension developed in the string is \( T = 11000 \, \text{N} \).

### Conclusion:
The tension in the string connected to the lift is **11000 N**.

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