COMEDK · Physics · 3. Motion In One Dimension

A bullet moving with a speed of \(100 \mathrm{~ms}^{-1}\) can just penetrate two planks of equal thickness.
Then, the number of such planks penetrated by the same bullet when the speed is doubled will be

A 4
B 8
C 6
D 10

Verified Solution

Answer & Solution

Correct Answer

(B) 8

Step-by-step Solution

Detailed explanation

Given, velocity of the bullet \(v=100 \mathrm{~ms}^{-1}\) Let, thickness of one plank, \(t=s\) According to third equation of motion, we get \(v^{2}-u^{2}=2 a s\) \((0)-(100)^{2}=2 \times a \times(2 s)\) ( \(\because\) two planks are penetrated)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A bullet moving with a speed of \(100 \mathrm{~ms}^{-1}\) can just penetrate two planks of equal thickness.Then, the number of such planks penetrated by the same bullet when the speed is doubled will be

Step-by-step Solution

A bullet moving with a speed of \(100 \mathrm{~ms}^{-1}\) can just penetrate two planks of equal thickness.
Then, the number of such planks penetrated by the same bullet when the speed is doubled will be