An elevator weighing 6000 kg is pulled upward by a cable with an acceleration of `5ms^(-2)` . Taking g to be `10 ms^(-2)` , then the tension in the cable is

Options

A. 6000 N
B. 9000 N
C. 60000 N
D. 90000 N

Answer

To find the tension in the cable pulling the elevator upward, we can follow these steps:

### Step 1: Identify the forces acting on the elevator
The forces acting on the elevator are:
1. The tension (T) in the cable acting upward.
2. The weight of the elevator (W) acting downward, which can be calculated using the formula:
\[ W = mg \]
where \( m \) is the mass of the elevator and \( g \) is the acceleration due to gravity.

### Step 2: Calculate the weight of the elevator
Given:
- Mass of the elevator, \( m = 6000 \, \text{kg} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

Calculating the weight:
\[ W = mg = 6000 \, \text{kg} \times 10 \, \text{m/s}^2 = 60000 \, \text{N} \]

### Step 3: Apply Newton's second law
According to Newton's second law, the net force acting on the elevator can be expressed as:
\[ F_{\text{net}} = T - W \]
Since the elevator is accelerating upward with an acceleration \( a = 5 \, \text{m/s}^2 \), we can set up the equation:
\[ F_{\text{net}} = ma \]
Substituting the expressions for \( F_{\text{net}} \):
\[ T - W = ma \]

### Step 4: Substitute the known values into the equation
We already calculated \( W \) and we know \( m \) and \( a \):
\[ T - 60000 \, \text{N} = 6000 \, \text{kg} \times 5 \, \text{m/s}^2 \]
Calculating \( ma \):
\[ ma = 6000 \, \text{kg} \times 5 \, \text{m/s}^2 = 30000 \, \text{N} \]

### Step 5: Solve for tension (T)
Now substituting back into the equation:
\[ T - 60000 \, \text{N} = 30000 \, \text{N} \]
Adding \( 60000 \, \text{N} \) to both sides:
\[ T = 30000 \, \text{N} + 60000 \, \text{N} = 90000 \, \text{N} \]

### Conclusion
The tension in the cable is:
\[ \boxed{90000 \, \text{N}} \]

---