A bullet moving with a speed of `100 ms^(-1)` can just penetrate into two planks of equal thickness. Then the number of such planks, if speed is doubled will be .

Options

A. a)`6`
B. b)`10`
C. c)`4`
D. d) `8`

Explanation

To solve the problem step by step, let's analyze the situation:

### Given:
- Initial speed of the bullet, \( u_1 = 100 \, \text{m/s} \)
- The bullet can penetrate into \( n_1 = 2 \) planks.

### To Find:
- The number of planks \( n_2 \) the bullet can penetrate when its speed is doubled, \( u_2 = 200 \, \text{m/s} \).

### Step 1: Understanding the relationship between speed and penetration depth
The penetration depth of the bullet into the planks is related to its initial speed. According to the physics of motion, the distance a bullet travels before coming to rest is proportional to the square of its initial speed. This can be expressed as:

\[ s \propto u^2 \]

Where \( s \) is the distance penetrated and \( u \) is the initial speed.

### Step 2: Setting up the proportionality for both cases
For the first case (initial speed):
\[ s_1 \propto u_1^2 \]
For the second case (doubled speed):
\[ s_2 \propto u_2^2 \]

### Step 3: Relating the two cases
We can express the ratio of the distances penetrated in terms of the speeds:
\[ \frac{s_2}{s_1} = \frac{u_2^2}{u_1^2} \]

### Step 4: Substituting the values
Substituting the known values:
- \( u_1 = 100 \, \text{m/s} \)
- \( u_2 = 200 \, \text{m/s} \)

We get:
\[ \frac{s_2}{s_1} = \frac{(200)^2}{(100)^2} = \frac{40000}{10000} = 4 \]

### Step 5: Finding the new penetration depth
Since the bullet penetrates 2 planks initially (\( s_1 = 2 \) planks), we can find \( s_2 \):
\[ s_2 = 4 \cdot s_1 = 4 \cdot 2 = 8 \, \text{planks} \]

### Conclusion
Thus, when the speed of the bullet is doubled, it can penetrate into **8 planks**.

### Final Answer:
The number of planks the bullet can penetrate when its speed is doubled is **8 planks**.

---