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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीA projectile of mass \( 3m \) is fired from the origin with speed \( u \) at an angle of \( 45^\circ \) to the horizontal. At the highest point of its trajectory, it explodes into two fragments of mass \( m \) and \( 2m \). If the fragment of mass \( m \) immediately falls vertically downwards to the ground, at what horizontal distance from the origin does the fragment of mass \( 2m \) land? (Neglect air resistance, \( R \) is original range).
Correct answer · Option 3
\( \frac{5}{4}R \)
Explanation
Because explosion involves internal forces, the centre of mass lands at \( X_{\text{cm}} = R \). The fragment \( m \) falls straight down from the apex, so it lands at \( x_1 = R/2 \). Using \( X_{\text{cm}} = \frac{m x_1 + 2m x_2}{3m} \implies R = \frac{m(R/2) + 2m x_2}{3m} \implies 3R = \frac{R}{2} + 2x_2 \implies 2x_2 = \frac{5R}{2} \implies x_2 = \frac{5}{4}R \).
