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Physics
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Center of Mass, Momentum and Collision

NEET · Physics · Center of Mass, Momentum and Collision

A ball of mass 0.3 kg strikes a rigid vertical wall with a speed of...

A ball of mass 0.3 kg0.3 \text{ kg} strikes a rigid vertical wall with a speed of 10 m s−110 \text{ m s}^{-1} at an angle of 30∘30^\circ with the surface of the wall. It rebounds with the same speed and at the same angle. The magnitude of the impulse imparted to the ball by the wall is:

Options

  1. A0 kg m s−10 \text{ kg m s}^{-1}
  2. B1.5 kg m s−11.5 \text{ kg m s}^{-1}
  3. C33 kg m s−13\sqrt{3} \text{ kg m s}^{-1}
  4. D3 kg m s−13 \text{ kg m s}^{-1}

Correct answer

D. 3 kg m s−13 \text{ kg m s}^{-1}

Step-by-step solution

Let the wall be along the y-axis and the normal to the wall be along the x-axis.

The angle made by the velocity vector with the surface of the wall is θ=30∘\theta = 30^\circ.

The component of velocity perpendicular to the wall is v⊥=vsin⁡30∘v_{\perp} = v \sin 30^\circ.
The component of velocity parallel to the wall is v∥=vcos⁡30∘v_{\parallel} = v \cos 30^\circ.

During the collision, the parallel component remains unchanged, while the perpendicular component reverses its direction.

Initial momentum perpendicular to the wall, pi=mvsin⁡30∘p_{i} = m v \sin 30^\circ
Final momentum perpendicular to the wall, pf=−mvsin⁡30∘p_{f} = -m v \sin 30^\circ

Magnitude of impulse = Change in momentum = ∣pf−pi∣=2mvsin⁡30∘|p_{f} - p_{i}| = 2 m v \sin 30^\circ

Impulse =2×0.3×10×12=3 kg m s−1= 2 \times 0.3 \times 10 \times \dfrac{1}{2} = 3 \text{ kg m s}^{-1}.

Answer: 3 kg m s−13 \text{ kg m s}^{-1}
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