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. 4
B. 8
C. 6
D. 10

Explanation

To solve the problem step-by-step, we will analyze the motion of the bullet as it penetrates the planks and how the distance it travels relates to its speed.

### Step 1: Understand the Initial Conditions
The bullet penetrates 2 planks of equal thickness at an initial speed of \(100 \, \text{m/s}\). Let the thickness of each plank be \(B\). Therefore, the total distance the bullet travels through the planks is \(2B\).

### Step 2: Use the Kinematic Equation
We can use the kinematic equation for uniformly decelerated motion:
\[ v^2 = u^2 - 2as \]
where:
- \(v\) is the final velocity (0, since the bullet stops),
- \(u\) is the initial velocity (100 m/s),
- \(a\) is the deceleration,
- \(s\) is the distance traveled (which is \(2B\)).

Rearranging the equation gives us:
\[ 0 = (100)^2 - 2a(2B) \]
This simplifies to:
\[ 10000 = 4aB \]
From this, we can express \(a\):
\[ a = \frac{10000}{4B} = \frac{2500}{B} \]

### Step 3: Analyze the New Conditions
Now, if the speed of the bullet is doubled, the new speed \(u' = 200 \, \text{m/s}\). We want to find out how many planks the bullet can penetrate at this new speed.

### Step 4: Apply the Kinematic Equation Again
Using the same kinematic equation for the new speed:
\[ v^2 = u'^2 - 2as' \]
where \(s'\) is the new distance traveled. Setting \(v = 0\) gives us:
\[ 0 = (200)^2 - 2a s' \]
This simplifies to:
\[ 40000 = 2a s' \]
Substituting \(a = \frac{2500}{B}\) into the equation:
\[ 40000 = 2 \left(\frac{2500}{B}\right) s' \]
This simplifies to:
\[ 40000 = \frac{5000 s'}{B} \]
Rearranging gives:
\[ s' = \frac{40000 B}{5000} = 8B \]

### Step 5: Calculate the Number of Planks
Since each plank has a thickness \(B\), the number of planks \(N\) that can be penetrated is:
\[ N = \frac{s'}{B} = \frac{8B}{B} = 8 \]

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

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