Q.36 Physics ⭐ 360° Option Elimination Active

NEET 2023 Physics Question 36 Solution

Topic: Motion in a Straight Line · Official NTA Booklet Code G5

Question

A bullet from a gun is fired on a rectangular wooden block with velocity u. When bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes u/3. Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:

✓

Verified Against NTA Final Answer Key

Option (2) : 27 cm

📚 Motion in a Straight Line Medium

📋 Given Parameters & Problem Setup

Initial bullet velocity u

Distance travelled in stage 1 (s₁) 24 cm

Velocity after stage 1 (v₁) u / 3

Final velocity at other end (v₂) 0 (comes to rest)

⚡

The 30-Second Exam Hall Shortcut: ⚡ Kinematic Ratio Hack: v² = u² - 2as

⏱️ Save ~60 seconds

Kinetic energy lost in 24 cm is u² - (u/3)² = (8/9)u². Remaining KE is (1/9)u² (which is 1/8th of the lost KE). Thus extra distance = 24 / 8 = 3 cm. Total length = 24 + 3 = 27 cm in 20 seconds!

1 Work done by retarding force is proportional to distance: F · s = ΔK.

2 Initial KE is proportional to u².

3 After 24 cm, KE is proportional to (u/3)² = u² / 9.

4 KE lost over 24 cm = u² - u²/9 = (8/9) u² ⟹ (8/9) u² requires 24 cm.

5 Therefore, each (1/9) u² of kinetic energy requires 24 / 8 = 3 cm of penetration.

6 The remaining kinetic energy to be lost before stopping is exactly (1/9) u².

7 Additional distance = 3 cm ⟹ Total length of block = 24 cm + 3 cm = 27 cm.

8 Select Option (2) 27 cm!

🛡️

Why You Can 100% Trust This Shortcut: Work-Energy Theorem / Kinematics (Uniform retarding force produces uniform loss of kinetic energy directly proportional to penetration distance).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Application of Third Equation of Motion to First Stage

Assuming a uniform resisting force and therefore a constant deceleration a throughout the wooden block, use the third equation of motion v² = u² - 2as for the first stage where the bullet enters with velocity u, travels s₁ = 24 cm, and reduces its velocity to v₁ = u/3:

\left(\frac{u}{3}\right)^2 = u^2 - 2a s_1 \implies \frac{u^2}{9} = u^2 - 2a (24)

Step 2

Isolation of Deceleration Term (2a)

Rearranging the equation to find the retarding acceleration term 2a:

48a = u^2 - \frac{u^2}{9} = \frac{8}{9} u^2 \implies 2a = \frac{8 u^2}{9 \times 24} = \frac{u^2}{27}

Step 3

Calculation of Total Stopping Distance s

For the bullet to come to complete rest (v = 0) from its initial velocity u over the total length of the block s:

0^2 = u^2 - 2a s \implies 2a s = u^2 \implies s = \frac{u^2}{2a}

Step 4

Substitution to Find Total Block Length

Substitute the value of 2a into the stopping distance equation:

s = \frac{u^2}{\frac{u^2}{27}} = 27\text{ cm}

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 (1)

✗ Incorrect

Verdict & Scientific Reason:

Overestimates stopping distance.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate made an arithmetic error in the fraction.

2 (2)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate total block length: 24 cm initial + 3 cm additional = 27 cm.

💡

Why this is airtight: None. Candidate correctly determined total stopping distance.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

This is merely the first-stage distance, not the total length.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate mistook stage 1 distance for total length.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Arithmetic slip.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate incorrectly calculated extra distance as 4 cm instead of 3 cm.

⚠️

NTA Trap Alert: Reporting Additional Distance (3 cm) Instead of Total Length (27 cm)

Some candidates solve for the additional distance Δs = 3 cm, and looking for 3 cm get confused when it is not in the options, or add it incorrectly to 24. The question specifically asks for the "TOTAL length of the block", which is 24 + 3 = 27 cm.

🛡️ How to avoid the -1 mark: Read the question prompt carefully: "total length of the block" means total stopping distance s = 27 cm.

📖

Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · Motion in a Straight Line Standard Benchmark

Core Scientific Principle Tested:

"Stopping distance under constant deceleration satisfies v² = u² - 2as, where distance is proportional to kinetic energy lost."

Syllabus Focus: Kinematic Equations for Uniformly Accelerated Motion

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 36 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Kinematic Ratio Hack: v² = u² - 2as

Step-by-Step Rigorous Workflow & Mathematical Proof

Application of Third Equation of Motion to First Stage

Isolation of Deceleration Term (2a)

Calculation of Total Stopping Distance s

Substitution to Find Total Block Length

360° Option Elimination Engine Key Feature

NTA Trap Alert: Reporting Additional Distance (3 cm) Instead of Total Length (27 cm)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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