A man is standing on a weighing machine placed in a lift. When stationary his weight is recorded as 40 kg . If the lift is accelerated upwards with an acceleration of `2m//s^(2)` , then the weight recorded in the machine will be `(g=10m//s^(2))`

Options

A. 32 kg
B. 40 kg
C. 42 kg
D. 48 kg

Answer

To solve the problem, we need to determine the weight recorded by the weighing machine when the lift is accelerating upwards. Here are the steps to arrive at the solution:

### Step 1: Understand the Initial Condition
When the lift is stationary, the weight recorded by the weighing machine is equal to the gravitational force acting on the man. This is given by:
\[ W = mg \]
where:
- \( m = 40 \, \text{kg} \) (mass of the man)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

### Step 2: Calculate the Gravitational Force
Using the values provided:
\[ W = 40 \, \text{kg} \times 10 \, \text{m/s}^2 = 400 \, \text{N} \]

### Step 3: Analyze the Situation When the Lift is Accelerating Upwards
When the lift accelerates upwards with an acceleration \( a = 2 \, \text{m/s}^2 \), the effective weight (normal force \( N \)) recorded by the weighing machine will change. The net force acting on the man can be expressed as:
\[ N - mg = ma \]

### Step 4: Rearranging the Equation
Rearranging the equation gives us:
\[ N = mg + ma \]

### Step 5: Substitute the Values
Now, substituting the values into the equation:
- \( m = 40 \, \text{kg} \)
- \( g = 10 \, \text{m/s}^2 \)
- \( a = 2 \, \text{m/s}^2 \)

We get:
\[ N = 40 \, \text{kg} \times 10 \, \text{m/s}^2 + 40 \, \text{kg} \times 2 \, \text{m/s}^2 \]
\[ N = 400 \, \text{N} + 80 \, \text{N} \]
\[ N = 480 \, \text{N} \]

### Step 6: Convert the Normal Force to Mass
To find the weight recorded by the weighing machine in terms of mass, we convert the normal force back to mass using:
\[ \text{Mass} = \frac{N}{g} \]
\[ \text{Mass} = \frac{480 \, \text{N}}{10 \, \text{m/s}^2} = 48 \, \text{kg} \]

### Final Answer
Thus, the weight recorded in the machine when the lift is accelerating upwards is **48 kg**.

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