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

Options

A. `2cms^(-1)`
B. `20cms^(-1)`
C. `200cms^(-1)`
D. `2000cms^(-1)`

Answer

To solve the problem step by step, we will follow the principles of Newton's laws of motion and the basic equations of motion.

### Step 1: Understand the given data
- Force (F) = 100 dynes
- Mass (m) = 5 grams
- Time (t) = 10 seconds
- Initial velocity (u) = 0 (the particle is at rest)

### Step 2: Convert units
We need to convert the force from dynes to Newtons and the mass from grams to kilograms for consistency in SI units.
- 1 dyne = \(10^{-5}\) Newtons
- 1 gram = \(10^{-3}\) kilograms

Thus,
- Force in Newtons:
\[ F = 100 \, \text{dynes} = 100 \times 10^{-5} \, \text{N} = 0.001 \, \text{N} \]
- Mass in kilograms:
\[ m = 5 \, \text{grams} = 5 \times 10^{-3} \, \text{kg} = 0.005 \, \text{kg} \]

### Step 3: Calculate acceleration
Using Newton's second law of motion, \( F = ma \), we can find the acceleration (a):
\[ a = \frac{F}{m} \]
Substituting the values:
\[ a = \frac{0.001 \, \text{N}}{0.005 \, \text{kg}} = 0.2 \, \text{m/s}^2 \]

### Step 4: Use the equation of motion to find final velocity
We will use the first equation of motion:
\[ v = u + at \]
Where:
- \( v \) = final velocity
- \( u \) = initial velocity = 0
- \( a \) = acceleration = 0.2 m/s²
- \( t \) = time = 10 seconds

Substituting the values:
\[ v = 0 + (0.2 \, \text{m/s}^2 \times 10 \, \text{s}) = 2 \, \text{m/s} \]

### Step 5: Convert the final velocity to centimeters per second
Since 1 m = 100 cm, we convert the velocity:
\[ v = 2 \, \text{m/s} = 2 \times 100 \, \text{cm/s} = 200 \, \text{cm/s} \]

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

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