Particles of mass 2 M, m and M are, respectively, at point A, B and C with A B=(1)/(2)(B C) ·m i

step 1 In this problem I can write the value of FBA, portion b due to a is equal to G to capital M smal

Particles of mass 2 M, m and M are, respectively, at point...

Particles of mass $2 M, m$ and $M$ are, respectively, at point $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ with $A B=\frac{1}{2}(B C) \cdot m$ is very much smaller than $M$ and at time $t=0$, they are all at rest as given in Fig. 7.10. At subsequent times before any collision takes place. (A) $m$ will remain at rest. (B) $m$ will move towards $M$. (C) $m$ will move towards $2 M$. (D) $m$ will have oscillatory motion.

Particles of mass $2 M, m$ and $M$ are, respectively, at point $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ with $A B=\frac{1}{2}(B C) \cdot m$ is very much smaller than $M$ and at time $t=0$, they are all at rest as given in Fig. 7.10. At subsequent times before any collision takes place.
(A) $m$ will remain at rest.
(B) $m$ will move towards $M$.
(C) $m$ will move towards $2 M$.
(D) $m$ will have oscillatory motion.

Key Concepts

Negligible Mass Approximation

In systems where one of the masses is significantly smaller than the others, its gravitational influence on the larger bodies can be ignored. This simplification allows one to treat the motion of the small mass as being dictated solely by the gravitational fields of the larger masses, without affecting them.

Inverse-Square Law and Distance Dependence

Gravitational forces diminish with the square of the distance between masses, meaning that even small changes in separation distance can lead to large differences in force magnitude. Understanding this dependence is crucial for analyzing how variations in distances between masses affect the net force direction and strength.

Newton's Law of Universal Gravitation

This principle states that every pair of masses exerts an attractive force on each other that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. It is essential for calculating the gravitational force contributions from different masses in a multi-body system.

Superposition Principle in Gravitational Interactions

When multiple masses act on a single object, the total gravitational force experienced by that object is the vector sum of the individual forces due to each mass. This concept is critical when determining the net force and the subsequent motion of a test mass in the presence of several other masses.

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