Two masses \( 2 m \) and \( m \) are connected by an inextensible light string. The string is pa...

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Two masses \( 2 m \) and \( m \) are connected by an inextensible light string. The string is passing over a light frictionless pulley. The mass \( 2 m \) is resting on a surface and mass \( m \) is hanging in air as shown in figure. A particle of mass \( m \) strikes the mass \( m \) from below in case (I) with a velocity \( v_{0} \) and in case (II) strikes mass \( m \) with a velocity \( v_{0} \) from top and sticks to it.
(1) The conservation of linear momentum can be applied in both the cases just before and just after collision.
(2) The conservation of linear momentum can be applied in case I but cannot be applied in case II just before and just after collision.
(3) The ratio of velocities of mass \( m \) just after collision in first and second cases is \( 1 / 2 \).
(4) The ratio of velocities of mass \( m \) just after collision in first and second case is 2 .
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