Two identical billiard balls strike a smooth rigid wall with equal speeds u. Ball A strikes head-on (normal incidence); ball B strikes at 30° to the wall normal and reflects symmetrically. The ratio of impulse magnitudes |J_A| : |J_B| on the balls is:
A1 : 1
B2 : √3
C1 : cos30°
D√3 : 1
Answer & Solution
Correct answer: B. 2 : √3
1. For head-on collision (A): Δp_x = m u − (− m u) = 2 m u. So |J_A| = 2 m u.
2. For oblique reflection (B): only the x-component (normal) reverses. Δp_x = 2 m u cos30°.
3. Δp_y = 0 because the tangential component is unchanged.
4. |J_B| = 2 m u cos30° = 2 m u · (√3/2) = √3 m u.
5. Ratio |J_A| : |J_B| = 2 m u : √3 m u = 2 : √3.
_Source: NCERT Class 11 Physics Ch 4 "Laws of Motion", Example 4.5, p. 57_
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