If a body of mass 5 kg initially at rest is acted upon by a force of 50 dyne for 3s, then the impulse will be

Options

A. `0.98xx10^(-3)Ns`
B. `1.5xx10^(-3) Ns`
C. `2xx10^(-3)Ns`
D. `2.5xx10^(-3)Ns`

Explanation

To solve the problem, we need to calculate the impulse experienced by a body of mass 5 kg when a force of 50 dyne acts on it for 3 seconds. Here’s the step-by-step solution:

### Step 1: Understand the concept of impulse
Impulse is defined as the product of force and the time duration for which the force acts. Mathematically, it can be expressed as:
\[ \text{Impulse} = \text{Force} \times \text{Time} \]

### Step 2: Convert the force from dyne to newton
The force given is 50 dyne. We need to convert this value into newtons. The conversion factor is:
\[ 1 \text{ dyne} = 10^{-5} \text{ newton} \]
Thus,
\[ \text{Force} = 50 \text{ dyne} = 50 \times 10^{-5} \text{ newton} = 5 \times 10^{-4} \text{ newton} \]

### Step 3: Identify the time duration
The time duration for which the force acts is given as 3 seconds.

### Step 4: Substitute the values into the impulse formula
Now we can substitute the values of force and time into the impulse formula:
\[ \text{Impulse} = \text{Force} \times \text{Time} \]
\[ \text{Impulse} = (5 \times 10^{-4} \text{ N}) \times (3 \text{ s}) \]

### Step 5: Calculate the impulse
Now, performing the multiplication:
\[ \text{Impulse} = 15 \times 10^{-4} \text{ N·s} = 1.5 \times 10^{-3} \text{ N·s} \]

### Conclusion
The impulse experienced by the body is:
\[ \text{Impulse} = 1.5 \times 10^{-3} \text{ N·s} \]

### Final Answer
The correct option is \( 1.5 \times 10^{-3} \text{ N·s} \).

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