Two plates AB and CD are rigidly attached perpendicular to base of a massive box. Box is released on smooth inclined plane having angle of inclination $37 °$ . With what minimum speed (in m/s) with respect to box, a particle is to be projected from base of box so as to graze top points A and C of plates ? $A B = 2 m, C D = 3 m .$ Given separation between tops of plates is 3m.
Take $g = 10 m / s^{2} .$

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Detailed Solution

Acceleration of particle with respect box is along perpendicular to inclined plane
$v_{\min} = \sqrt{g \cos 37 ° (A B + C D + A C)} = \sqrt{8 (2 + 3 + 3)} = 8 m / s$

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