A particle of mass m is projected at an angle of 60^owith a velocity of 20 m/s relative to the ground from a plank of same mass m which is placed on a smooth surface initially plank was at rest. The minimum length of the plank for which the ball will fall on the plank itself is

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Since t h e e x t e r n a l f o r c e o n t h e s y s t e m i s z e r o , l o c a t i o n o f COM w i l l n o t s h i f t . ⇒ m 1 x 1 = m 2 x 2 m x = m L - x ⇒ x = L 2 s o p l a n k w i l l s h i f t b y L 2 t o w a r d s l e f t . N o w r a n g e R s h o u l d b e < _ L 2 ⇒ L = 2 R ⇒ L = 2 u 2 s i n 30 g = 40 3

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