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. We start with the following information:

1. The man's weight when the lift is stationary is recorded as 40 kg.
2. The acceleration of the lift when it moves upwards is \(2 \, \text{m/s}^2\).
3. The acceleration due to gravity \(g\) is given as \(10 \, \text{m/s}^2\).

### Step-by-Step Solution:

**Step 1: Calculate the man's mass.**
The weight recorded when the lift is stationary is given as 40 kg. The weight \(W\) in Newtons can be calculated using the formula:
\[ W = m \cdot g \]
Where \(m\) is the mass in kg and \(g\) is the acceleration due to gravity.
Since the weight is given in kg, we can convert it to Newtons:
\[ W = 40 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 400 \, \text{N} \]
Thus, the man's mass \(m\) is:
\[ m = 40 \, \text{kg} \]

**Step 2: Determine the effective weight when the lift accelerates upwards.**
When the lift accelerates upwards, the effective weight \(N\) (the normal force) can be calculated using the formula:
\[ N = m(g + a) \]
Where \(a\) is the acceleration of the lift.
Substituting the values:
\[ N = 40 \, \text{kg} \cdot (10 \, \text{m/s}^2 + 2 \, \text{m/s}^2) \]
\[ N = 40 \, \text{kg} \cdot 12 \, \text{m/s}^2 \]
\[ N = 480 \, \text{N} \]

**Step 3: Convert the effective weight back to mass.**
The weighing machine measures mass based on the weight it records. To find the mass recorded by the weighing machine, we use the formula:
\[ \text{Mass} = \frac{N}{g} \]
Substituting the values:
\[ \text{Mass} = \frac{480 \, \text{N}}{10 \, \text{m/s}^2} \]
\[ \text{Mass} = 48 \, \text{kg} \]

### Final Answer:
The weight recorded in the machine when the lift is accelerating upwards at \(2 \, \text{m/s}^2\) will be **48 kg**.