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One of two blocks is moved towards the other: how far the other must move to keep the centre of mass fixed

The same question, asked 2 times: 27 Jun 2022*, 4 Apr 2024. Every wording below, oldest first.

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  1. Question 1

    27 Jun 2022

    5
    Two blocks of masses 10 kg10\text{ }kg and 30 kg30\text{ }kg are placed on the same straight line with coordinates (0,0)cm(0,0)cm and (x,0)cm(x,0)cm respectively. The block of 10 kg10\text{ }kg is moved on the same line through a distance of 6 cm6\text{ }cm towards the other block. The distance through which the block of 30 kg30\text{ }kg must be moved to keep the position of centre of mass of the system unchanged is:

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  2. Question 2

    4 Apr 2024

    114
    In a system two particles of masses m1=3 kgm_{1}= 3\text{ }kg and m2=2 kgm_{2}= 2\text{ }kg are placed at certain distance from each other. The particle of mass m1m_{1} is moved towards the center of mass of the system through a distance 2 cm2\text{ }cm. In order to keep the center of mass of the system at the original position, the particle of mass m2m_{2} should move towards the center of mass by the distance ____ cmcm.