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

Options

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

Answer

To solve the problem of finding the tension in the supporting cable of the lift, we can follow these steps:

### Step 1: Identify the forces acting on the system
In this scenario, we have two main forces acting on the lift:
1. The weight of the lift (downward force) = mass of the lift × g = 940 kg × 10 m/s² = 9400 N
2. The weight of the person inside the lift (downward force) = mass of the person × g = 60 kg × 10 m/s² = 600 N

### Step 2: Calculate the total downward force
The total downward force (weight of the lift + weight of the person) can be calculated as:
Total downward force = Weight of lift + Weight of person
= 9400 N + 600 N = 10000 N

### Step 3: Determine the net force required for upward acceleration
The lift is accelerating upwards with an acceleration of 1 m/s². According to Newton's second law, the net force required to accelerate the system upwards can be calculated using the formula:
Net force = (Total mass) × (acceleration)
Where the total mass = mass of lift + mass of person = 940 kg + 60 kg = 1000 kg

Net force = 1000 kg × 1 m/s² = 1000 N

### Step 4: Calculate the tension in the cable
The tension in the cable must overcome both the total weight of the system and provide the net upward force. Therefore, the tension (T) can be calculated as:
T = Total downward force + Net force
T = 10000 N + 1000 N = 11000 N

### Final Answer
The tension in the supporting cable is **11000 N**.

---