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NEET PHYSICSLAWS OF MOTIONMedium

Question

The average force necessary to stop a bullet of mass 20 g moving with a speed of 250 m/s, as it penetrates into the wood for a distance of 12 cm is:

A

2.2 × 10³ N

B

3.2 × 10³ N

C

4.2 × 10³ N

D

5.2 × 10³ N

Step-by-Step Solution

  1. Identify Given Values:
  • Mass (mm) = 20 g=0.02 kg20 \text{ g} = 0.02 \text{ kg}
  • Initial velocity (uu) = 250 m/s250 \text{ m/s}
  • Final velocity (vv) = 0 m/s0 \text{ m/s} (stops)
  • Distance (ss) = 12 cm=0.12 m12 \text{ cm} = 0.12 \text{ m}

  1. Method 1: Work-Energy Theorem The work done by the resistive force (FF) equals the change in kinetic energy [Source 93, 95]. W=ΔK=Kf−KiW = \Delta K = K_f - K_i −F⋅s=12mv2−12mu2-F \cdot s = \frac{1}{2}mv^2 - \frac{1}{2}mu^2 F⋅s=12mu2F \cdot s = \frac{1}{2}mu^2 F=mu22sF = \frac{mu^2}{2s}

  2. Calculation: F=0.02×(250)22×0.12F = \frac{0.02 \times (250)^2}{2 \times 0.12} F=0.02×625000.24F = \frac{0.02 \times 62500}{0.24} F=12500.24≈5208.33 NF = \frac{1250}{0.24} \approx 5208.33 \text{ N}

  3. Scientific Notation: F≈5.2×103 NF \approx 5.2 \times 10^3 \text{ N} (This approach aligns with Example 4.2 in Source 79, which uses kinematic equations and Newton's second law to solve a similar bullet-block problem).

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from LAWS OF MOTION. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSLAWS OF MOTIONaveragenecessarybulletmovingpenetrates

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