The velocity of a bullet is reduced from `200 m//s` to `100 m//s` while travelling through a wooden block of thickness `10 cm`. The retardation, assuming it to be uniform, will be.

Options

A. `10 xx 10^4 m//s^2`
B. `12 xx 10^4 m//s^2`
C. `12.5 xx 10^4 m//s^2`
D. `15 xx 10^4 m//s^2`

Explanation

To find the uniform retardation of the bullet as it travels through the wooden block, we can use the kinematic equation:

\[ v^2 = u^2 + 2as \]

Where:
- \( v \) = final velocity (100 m/s)
- \( u \) = initial velocity (200 m/s)
- \( a \) = acceleration (which will be negative for retardation)
- \( s \) = distance traveled (10 cm = 0.1 m)

### Step 1: Identify the known values
- Initial velocity \( u = 200 \, \text{m/s} \)
- Final velocity \( v = 100 \, \text{m/s} \)
- Distance \( s = 10 \, \text{cm} = 0.1 \, \text{m} \)

### Step 2: Rearrange the kinematic equation for \( a \)
Since we are looking for retardation (which is negative acceleration), we can rearrange the equation:
\[ v^2 = u^2 + 2as \]
This can be rearranged to solve for \( a \):
\[ a = \frac{v^2 - u^2}{2s} \]

### Step 3: Substitute the known values into the equation
Substituting the values we have:
\[ a = \frac{(100)^2 - (200)^2}{2 \times 0.1} \]

### Step 4: Calculate the squares
Calculating the squares:
\[ (100)^2 = 10000 \]
\[ (200)^2 = 40000 \]

### Step 5: Substitute the squares back into the equation
Now substituting these values back into the equation:
\[ a = \frac{10000 - 40000}{2 \times 0.1} \]
\[ a = \frac{-30000}{0.2} \]

### Step 6: Calculate the value of \( a \)
Now, calculating \( a \):
\[ a = -150000 \, \text{m/s}^2 \]

### Conclusion
The retardation of the bullet is \( 150000 \, \text{m/s}^2 \).