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Two particles of mass 1 kg and 3 kg move towards each other under their mutual force of attraction. No other force acts on them. When the relative velocity of approach of the two particles is 2m//s, their centre of mass has a velocity of 0.5 m/s. When the relative velocity of approach becomes 3 m/s. When the relative velocity of approach becomes 3m/s, the velocity of the centre of mass is 0.75 m/s.

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To solve the problem, we need to analyze the motion of the two particles and the implications of their velocities on the center of mass (CM) of the system. ### Step-by-Step Solution: 1. **Understanding the System**: We have two particles with masses \( m_1 = 1 \, \text{kg} \) and \( m_2 = 3 \, \text{kg} \). They are moving towards each other due to their mutual gravitational attraction. 2. **Finding the Center of Mass Velocity**: ...
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Knowledge Check

  • Two particles of mass 1 kg and 3 kg move towards each other under their mutual force of attraction . No other force acts on them . When the relative velocity of approach of two particles is 2 ms^(-1) , their centre of mass has a velocity of 0.5 ms^(-1) when the relative velocity of approach becomes 3 m , the velocity of the center of mass will be

    A
    `0.75 ms ^(-1)`
    B
    `0.5 ms ^(-1)`
    C
    `10 ms ^(-1)`
    D
    `1.25 ms ^(-1)`

  • Statement-1: Two particles of mass 1 kg and 3 kg move towards each other under their mutual force of attraction. No other force acts on them. When the relative velocity of approach of the two particles is 2 m//s , their centre of mass has a velocity of 0.5 m//s . When the relative velocity of approach becomes 3 m//s the velocity of the centre of mass is 0.75 m//s . Statement-2: The total kinetic energy as seen from ground is 1/2muv_(rel)^(2)+1/2mv_(c)^(2) and in absence of external force, total energy remains conserved.

    A
    Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
    B
    Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
    C
    Statement-1 is true, statement-2 is false.
    D
    Statement -1 is false, statement -2 is true.

  • Two particles of mass m_(1) and m_(2) , approach each other due to their mutual gravitational attraction only. Then

    A
    acceleration of both the particles are equal.
    B
    acceleration of the particle of mass `m_(1)` is proportional to `m_(1)`
    C
    acceleration the particle of mass `m_(1)` is proportional to `m_(2)`.
    D
    accelaration of the particle of mass `m_(1)` is inversely proportional to `m_(1)`.

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