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. 11000 N
D. 10, 000 N

Explanation

To find the tension developed in the string connected to the lift, we can follow these steps:

### Step 1: Identify the forces acting on the lift
The forces acting on the lift are:
- The tension (T) in the string acting upwards.
- The weight of the lift (mg) acting downwards, where m is the mass of the lift and g is the acceleration due to gravity.

### Step 2: Write the equation of motion
Since the lift is moving upwards with an acceleration (a), we can apply Newton's second law of motion. The net force acting on the lift can be expressed as:
\[ T - mg = ma \]

### Step 3: Substitute the known values
Given:
- Mass of the lift, \( m = 1000 \, \text{kg} \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)
- Acceleration of the lift, \( a = 1 \, \text{m/s}^2 \)

Now, calculate the weight of the lift:
\[ mg = 1000 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 9800 \, \text{N} \]

### Step 4: Rearrange the equation to solve for tension (T)
From the equation of motion:
\[ T = ma + mg \]

### Step 5: Substitute the values into the equation
Substituting the values we have:
\[ T = (1000 \, \text{kg} \times 1 \, \text{m/s}^2) + 9800 \, \text{N} \]
\[ T = 1000 \, \text{N} + 9800 \, \text{N} \]
\[ T = 10800 \, \text{N} \]

### Final Answer
The tension developed in the string is \( T = 10800 \, \text{N} \).

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