The mass of a lift if 600kg and it is moving upwards with a uniform acceleration of `2m//s^(2)`. Then the tension in the cable of the lift is `:`

Options

A. (a)7200 N
B. (b)5900 N
C. (c)4700 N
D. (d)zero N

Answer

To find the tension in the cable of the lift, we can follow these steps:

### Step 1: Identify the forces acting on the lift
The forces acting on the lift are:
1. The tension (T) in the cable acting upwards.
2. 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: Calculate the weight of the lift
The weight of the lift can be calculated using the formula:
\[ \text{Weight (mg)} = m \cdot g \]
Given:
- Mass (m) = 600 kg
- Acceleration due to gravity (g) = 10 m/s²

Calculating the weight:
\[ mg = 600 \, \text{kg} \times 10 \, \text{m/s}^2 = 6000 \, \text{N} \]

### Step 3: Apply Newton's second law of motion
According to Newton's second law, the net force acting on the lift is equal to the mass of the lift multiplied by its acceleration (a):
\[ \text{Net Force} = m \cdot a \]
The lift is moving upwards with an acceleration of 2 m/s², so:
\[ \text{Net Force} = 600 \, \text{kg} \times 2 \, \text{m/s}^2 = 1200 \, \text{N} \]

### Step 4: Set up the equation for tension
The net force acting on the lift can also be expressed as the difference between the tension in the cable and the weight of the lift:
\[ T - mg = ma \]
Substituting the known values:
\[ T - 6000 \, \text{N} = 1200 \, \text{N} \]

### Step 5: Solve for tension (T)
Rearranging the equation to find T:
\[ T = mg + ma \]
Substituting the values:
\[ T = 6000 \, \text{N} + 1200 \, \text{N} = 7200 \, \text{N} \]

### Conclusion
The tension in the cable of the lift is:
\[ \boxed{7200 \, \text{N}} \]

---