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NEET PHYSICSLAWS OF MOTIONMedium

Question

A 0.5 kg0.5 \text{ kg} ball moving with a speed of 12 m/s12 \text{ m/s} strikes a hard wall at an angle of 30∘30^{\circ} with the wall. It is reflected with the same speed and at the same angle. If the ball is in contact with the wall for 0.25 s0.25 \text{ s}, the average force acting on the wall is:

A

48 N

B

24 N

C

12 N

D

96 N

Step-by-Step Solution

  1. Identify the Angle: The problem states the ball strikes at an angle of 30∘30^{\circ} with the wall. This corresponds to a glancing angle. The angle with the normal (perpendicular to the wall) is θ=90∘−30∘=60∘\theta = 90^{\circ} - 30^{\circ} = 60^{\circ}. Alternatively, one can resolve components directly using the angle with the wall.
  2. Change in Momentum (Impulse): The force exerted by the wall changes the momentum of the ball only in the direction perpendicular to the wall.
  • Component perpendicular to the wall: v⊥=vsin⁡(30∘)v_{\perp} = v \sin(30^{\circ}) (using angle with wall) or vcos⁡(60∘)v \cos(60^{\circ}) (using angle with normal).
  • Calculation of Impulse (Δp\Delta p): Δp=m(v⊥,final−v⊥,initial)\Delta p = m(v_{\perp, final} - v_{\perp, initial}) Δp=m(vsin⁡30∘−(−vsin⁡30∘))=2mvsin⁡30∘\Delta p = m(v \sin 30^{\circ} - (-v \sin 30^{\circ})) = 2mv \sin 30^{\circ} Substituting values: Δp=2×0.5×12×0.5=6 kg m/s\Delta p = 2 \times 0.5 \times 12 \times 0.5 = 6 \text{ kg m/s}.
  1. Calculate Average Force: According to Newton's Second Law: Favg=ΔpΔtF_{avg} = \frac{\Delta p}{\Delta t} Favg=60.25=24 NF_{avg} = \frac{6}{0.25} = 24 \text{ N} (Reference: NCERT Class 11, Physics Part I, Chapter 5, Section 5.7 regarding Impulse).

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 MOTIONmovingstrikesreflectedcontactaverage

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