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

Options

A. 8600N
B. 9680N
C. 10340N
D. 1200N

Explanation

To find the tension in the supporting cable of the lift, we can use Newton's second law of motion. Here’s the step-by-step solution:

### Step 1: Identify the known values
- Mass of the person (m) = 940 kg
- Acceleration of the lift (a) = 1.0 m/s²
- Acceleration due to gravity (g) = 10 m/s²

### Step 2: Calculate the weight of the person
The weight (W) of the person can be calculated using the formula:
\[ W = m \cdot g \]
Substituting the known values:
\[ W = 940 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 9400 \, \text{N} \]

### Step 3: Apply Newton's second law
When the lift accelerates upwards, the net force acting on the person is given by:
\[ F_{\text{net}} = T - W \]
Where:
- \( T \) is the tension in the cable
- \( W \) is the weight of the person

According to Newton's second law:
\[ F_{\text{net}} = m \cdot a \]
Thus, we can write:
\[ T - W = m \cdot a \]

### Step 4: Rearranging the equation to find tension
Rearranging the equation gives us:
\[ T = W + m \cdot a \]

### Step 5: Substitute the known values into the equation
Now, substitute the values of \( W \), \( m \), and \( a \):
\[ T = 9400 \, \text{N} + (940 \, \text{kg} \cdot 1.0 \, \text{m/s}^2) \]
\[ T = 9400 \, \text{N} + 940 \, \text{N} \]
\[ T = 10340 \, \text{N} \]

### Final Answer
The tension in the supporting cable is:
\[ T = 10340 \, \text{N} \]

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