A rigid ball of mass m strikes a rigid wall at 60° to the normal and gets reflected without loss of

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Question

A rigid ball of mass m strikes a rigid wall at 60° to the normal and gets reflected without loss of speed, as shown in the figure. The value of impulse imparted by the wall on the ball will be:

Accepted Answer

Correct Answer: C — mVStep-by-step Solution:Step 1: Resolve velocity into components.The ball strikes at 60° to the wall (i.e., 30° to the normal, or 60° to the normal depending on the figure convention).If the angle with the wall is 60°, then the angle with the normal is 30°.Component perpendicular to wall (normal): V cos 60° = V/2 (this reverses)Component parallel to wall (tangential): V sin 60° = V sqrt(3)/2 (unchanged)Step 2: Calculate change in momentum.Only the perpendicular component changes (reverses in direction):Change in perpendicular momentum = m(V/2) - m(-V/2) = mVThe parallel component does not change, so contributes zero impulse.Impulse = change in momentum = mVWhy other options are incorrect:Option A (mV/2): Uses only the change in one sign of V cos 60°, forgetting to account for the reversal (factor of 2).Option B (mV/sqrt(3)): Corresponds to the change in momentum if the angle with the normal were 60° (then perpendicular component = V cos 60° = V/2, change = mV, same result; but using sin gives mV sin 30° = mV/2... this option appears from an incorrect geometric analysis).Option D (2mV): Would be correct only if the ball bounced back along the normal (head-on collision, angle = 0°), where both approach and rebound velocity are V perpendicular to wall.Key Concept:Impulse = change in momentum (vector quantity): J = p_f - p_i.For elastic reflection from a rigid wall, speed is unchanged but the perpendicular component reverses while the parallel component is unchanged.Impulse = m × (change in velocity) = m × 2 × (perpendicular component of velocity) = 2mV cos theta_normal = mV (for 60° to wall, i.e., 30° to normal).The wall exerts force only in the normal direction.

A rigid ball of mass m strikes a rigid wall at 60° to the normal and gets reflected without loss of speed, as shown in the figure. The value of impulse imparted by the wall on the ball will be:

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A rigid ball of mass m strikes a rigid wall at 60° to the normal and gets reflected without loss of speed, as shown in the figure. The value of impulse imparted by the wall on the ball will be:

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Frequently Asked Questions