A person of mass `60kg` is inside a lift of mass `940kg` and presses the button on control panel. The lift starts moving upword with an acceleration `1.0m//s^(2)` . If `g=10m//s^(2)` , the tension in the supporting cable is.

Options

A. 9680 N
B. 11000 N
C. 1200 N
D. 8600 N

Answer

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

### Step 1: Identify the masses involved
The mass of the person inside the lift (m1) is given as 60 kg, and the mass of the lift (m2) is given as 940 kg.

### Step 2: Calculate the total mass
The total mass (M) of the system (person + lift) is:
\[ M = m1 + m2 = 60 \, \text{kg} + 940 \, \text{kg} = 1000 \, \text{kg} \]

### Step 3: Write down the forces acting on the system
When the lift moves upward with an acceleration (a), the forces acting on the system are:
- The tension (T) in the cable acting upward.
- The weight of the system (Mg) acting downward, where \( g = 10 \, \text{m/s}^2 \).

The weight of the system can be calculated as:
\[ W = Mg = 1000 \, \text{kg} \times 10 \, \text{m/s}^2 = 10000 \, \text{N} \]

### Step 4: Apply Newton's second law
According to Newton's second law, the net force (F_net) acting on the system is equal to the mass of the system multiplied by its acceleration:
\[ F_{\text{net}} = Ma \]
In this case, the net force can also be expressed as:
\[ F_{\text{net}} = T - W \]
Thus, we can write:
\[ T - W = Ma \]

### Step 5: Substitute the known values
Substituting the known values into the equation:
\[ T - 10000 \, \text{N} = 1000 \, \text{kg} \times 1 \, \text{m/s}^2 \]
\[ T - 10000 \, \text{N} = 1000 \, \text{N} \]

### Step 6: Solve for tension (T)
Now, we can solve for T:
\[ T = 10000 \, \text{N} + 1000 \, \text{N} \]
\[ T = 11000 \, \text{N} \]

### Final Answer
The tension in the supporting cable is:
\[ \boxed{11000 \, \text{N}} \]

---