Question

Consider a two particle system with particles having masses m1 and m2m1 and m2. If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle be moved, so as to keep the centre of mass at the same position ?

Answer 1

$\huge\mathfrak\red{hello}$

Answer 2

Homework or not, let me offer the path to the solution, not the solution itself. What you need to know is TWO things. First, when the masses are at rest at infinity, they have no kinetic and no potential energy, and also no momentum. As they approach each other, their (gravitational) potential energy becomes negative, but this will be balanced by increasing (positive) kinetic energy. Second, the total momentum of the two masses will remain zero. So if you have the formulae for gravitational potential energy, kinetic energy, and momentum handy, you can quickly write down TWO equations in TWO unknowns (the two velocities), solve them (they are very easy) and calculate the sum. Just beware of the signs, especially when you think about the momentum (the two masses move in opposite directions, hence the momentum of one must be subtracted from the other.)

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