A 60kg man is inside a lift which is moving up with an acceleration of `2.45 ms^(-2)`. The apparent percentage change in his weight is,

Options

A. `20%`
B. `25%`
C. `50%`
D. `75%`

Answer

To solve the problem step by step, we will calculate the apparent weight of the man in the lift and then determine the percentage change in his weight.

### Step 1: Calculate the actual weight of the man
The actual weight (W) of the man can be calculated using the formula:
\[ W = m \cdot g \]
where:
- \( m = 60 \, \text{kg} \) (mass of the man)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

Substituting the values:
\[ W = 60 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 600 \, \text{N} \]

### Step 2: Calculate the apparent weight of the man in the lift
When the lift is accelerating upwards, the apparent weight (W') can be calculated using the formula:
\[ W' = m \cdot (g + a) \]
where:
- \( a = 2.45 \, \text{m/s}^2 \) (acceleration of the lift)

Substituting the values:
\[ W' = 60 \, \text{kg} \cdot (10 \, \text{m/s}^2 + 2.45 \, \text{m/s}^2) \]
\[ W' = 60 \, \text{kg} \cdot 12.45 \, \text{m/s}^2 \]
\[ W' = 747 \, \text{N} \]

### Step 3: Calculate the percentage change in weight
The percentage change in weight can be calculated using the formula:
\[ \text{Percentage Change} = \frac{W' - W}{W} \times 100 \]

Substituting the values:
\[ \text{Percentage Change} = \frac{747 \, \text{N} - 600 \, \text{N}}{600 \, \text{N}} \times 100 \]
\[ \text{Percentage Change} = \frac{147 \, \text{N}}{600 \, \text{N}} \times 100 \]
\[ \text{Percentage Change} = 24.5\% \]

### Final Result
The apparent percentage change in his weight is approximately **25%**.

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