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NEET PHYSICSLAWS OF MOTIONEasy

Question

A 1 kg1 \text{ kg} object strikes a wall with velocity 1 ms−11 \text{ ms}^{-1} at an angle of 60∘60^\circ with the wall and reflects at the same angle. If it remains in contact with the wall for 0.1 s0.1 \text{ s}, then the force exerted on the wall is:

A

303 N30\sqrt{3} \text{ N}

B

zero

C

103 N10\sqrt{3} \text{ N}

D

203 N20\sqrt{3} \text{ N}

Step-by-Step Solution

  1. Identify Given Data:
  • Mass m=1 kgm = 1 \text{ kg} (inferred from input artifact '111').
  • Velocity v=1 m/sv = 1 \text{ m/s} (inferred from input artifact '111').
  • Angle with wall θ=60∘\theta = 60^\circ.
  • Time of contact Δt=0.1 s\Delta t = 0.1 \text{ s}.
  1. Analyze Momentum Change:
  • The component of velocity parallel to the wall (vcos⁡60∘v \cos 60^\circ) remains unchanged.
  • The component of velocity perpendicular to the wall (vsin⁡60∘v \sin 60^\circ) reverses direction.
  • Initial perpendicular momentum pi=mvsin⁡60∘p_i = m v \sin 60^\circ.
  • Final perpendicular momentum pf=−mvsin⁡60∘p_f = -m v \sin 60^\circ (taking opposite direction).
  • Change in momentum ∣Δp∣=∣pf−pi∣=2mvsin⁡60∘|\Delta p| = |p_f - p_i| = 2mv \sin 60^\circ [Source 133].
  1. Calculate Impulse: Δp=2×1×1×32=3 kg m/s\Delta p = 2 \times 1 \times 1 \times \frac{\sqrt{3}}{2} = \sqrt{3} \text{ kg m/s}
  2. Calculate Force:
  • Average force F=ΔpΔtF = \frac{\Delta p}{\Delta t}. F=30.1=103 NF = \frac{\sqrt{3}}{0.1} = 10\sqrt{3} \text{ N} [Source 132, 144]

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 MOTIONobjectstrikesvelocityreflectsremains

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