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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 3m/s, the velocity of the centre of mass is 0.75 m/s.

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To determine whether the given statement about the two particles is true or false, we can analyze the situation step by step. ### Step 1: Understand the System We have two particles with masses: - Mass \( m_1 = 1 \, \text{kg} \) - Mass \( m_2 = 3 \, \text{kg} \) These particles are moving towards each other under their mutual gravitational attraction, and no external forces are acting on them. ...
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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.

Two particles of masses 2 kg and 3 kg are at rest separated by 10 m. If they move towards each other under mutual force of attraction, the position of the point where they meet is

Knowledge Check

  • Two spheres of masses 2 M and M are intially at rest at a distance R apart. Due to mutual force of attraction, they approach each other. When they are at separation R/2, the acceleration of the centre of mass of sphere would be

    A
    `0m//s^(2)`
    B
    `gm//s^(2)`
    C
    `3g m//s^(2)`
    D
    `12 gm//s^(2)`

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