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NEET PHYSICSEasy

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]
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