A man of mass 60 kg climbed down using an elevator . The elevator had an acceleration of `4ms^(-2)` . If the acceleration due to gravity is `10 ms ^(-2)` , the man's apparent weight on his way down is

Options

A. (a)60 N
B. (b)240 N
C. (c)360 N
D. (d)840 N

Answer

To find the man's apparent weight while he is descending in the elevator, we can follow these steps:

### Step 1: Understand the Forces Acting on the Man
When the man is in the elevator, two main forces act on him:
1. The gravitational force acting downward, which is given by \( F_g = m \cdot g \).
2. The normal force acting upward, which we will denote as \( N \).

### Step 2: Identify the Given Values
- Mass of the man, \( m = 60 \, \text{kg} \)
- Acceleration of the elevator, \( a = 4 \, \text{m/s}^2 \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

### Step 3: Write the Equation for Apparent Weight
When the elevator accelerates downward, the apparent weight \( N \) can be calculated using the following equation derived from Newton's second law:
\[ N = m \cdot (g - a) \]
This equation states that the normal force (apparent weight) is equal to the gravitational force minus the force due to the elevator's acceleration.

### Step 4: Substitute the Values into the Equation
Now we can substitute the known values into the equation:
\[ N = 60 \, \text{kg} \cdot (10 \, \text{m/s}^2 - 4 \, \text{m/s}^2) \]
\[ N = 60 \, \text{kg} \cdot (6 \, \text{m/s}^2) \]

### Step 5: Calculate the Apparent Weight
Now we can perform the multiplication:
\[ N = 60 \cdot 6 = 360 \, \text{N} \]

### Conclusion
The man's apparent weight while descending in the elevator is \( 360 \, \text{N} \).