A force of 100 dynes acts on mass of 5 gm for 10 sec . The velocity produced is

Options

A. `2cm//sec`
B. `20cm//sec`
C. `200cm//sec`
D. `2000cm//sec`

Answer

To solve the problem step by step, we will use Newton's second law of motion and the equations of motion.

### Step 1: Identify the given values
- Force (F) = 100 dynes
- Mass (m) = 5 grams
- Time (t) = 10 seconds

### Step 2: Convert the mass from grams to kilograms (if necessary)
Since the problem is given in the CGS system, we can keep the mass in grams. However, if we were to convert it to kilograms for SI units:
- 5 grams = 0.005 kg (not necessary for this problem as we will use CGS units)

### Step 3: Calculate the acceleration using Newton's second law
Newton's second law states that:
\[ F = m \cdot a \]
Where:
- \( F \) is the force,
- \( m \) is the mass,
- \( a \) is the acceleration.

Rearranging the formula to find acceleration:
\[ a = \frac{F}{m} \]

Substituting the values:
\[ a = \frac{100 \text{ dynes}}{5 \text{ g}} = 20 \text{ cm/s}^2 \]

### Step 4: Use the equation of motion to find the final velocity
We will use the first equation of motion:
\[ v = u + at \]
Where:
- \( v \) is the final velocity,
- \( u \) is the initial velocity,
- \( a \) is the acceleration,
- \( t \) is the time.

Given that the initial velocity \( u = 0 \) (the block starts from rest), we can substitute the values:
\[ v = 0 + (20 \text{ cm/s}^2) \cdot (10 \text{ s}) \]
\[ v = 200 \text{ cm/s} \]

### Final Answer
The velocity produced is **200 cm/s**.

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