A man of weight mg is moving up in a rocket with acceleration 4 g . The apparent weight of the man in the rocket is

Options

A. Zero
B. 4 mg
C. 5 mg
D. mg

Answer

To find the apparent weight of a man moving up in a rocket with an acceleration of \(4g\), we can follow these steps:

### Step 1: Understand the Forces Acting on the Man
The man has a weight \(mg\) acting downwards due to gravity. When the rocket accelerates upwards with an acceleration of \(4g\), we need to consider the effect of this acceleration on the apparent weight of the man.

### Step 2: Calculate the Pseudo Force
When analyzing the situation from the perspective of the man inside the rocket (which is a non-inertial frame of reference), we introduce a pseudo force. The pseudo force \(F_p\) can be calculated using the formula:
\[ F_p = m \cdot a \]
where \(m\) is the mass of the man and \(a\) is the acceleration of the rocket. Here, \(a = 4g\).

Thus, the pseudo force acting on the man is:
\[ F_p = m \cdot (4g) = 4mg \]

### Step 3: Calculate the Apparent Weight
The apparent weight \(W'\) of the man in the rocket is the sum of the actual weight and the pseudo force:
\[ W' = mg + F_p \]
Substituting the value of the pseudo force:
\[ W' = mg + 4mg = 5mg \]

### Conclusion
Therefore, the apparent weight of the man in the rocket is:
\[ W' = 5mg \]

### Final Answer
The apparent weight of the man in the rocket is \(5mg\).

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