Ncert Exercises & Solutions

Particles of masses $2M, m$ and $M$ are respectively at points $A, B$ and $C$ with $A B = \dfrac{1}{2} \left( B C \right).$ The mass $m$ is much-much smaller than $M$ and at time $t = 0$ , they are all at rest as given in the figure. At subsequent times before any collision takes place,

1. $m$ will remain at rest.

2. $m$ will move towards $M.$

3. $m$ will move towards $2M.$

4. $m$ will have oscillatory motion.

(c) Hint: The motion of mass m will depend on the forces acting on it.

Step 1: Find the net force acting on mass m.

Force on B due to

$A = F_{B A} = \frac{G (2 M m)}{{(A B)}^{2}}$ towards BA

Force on B due to C

$= F = \frac{G M m}{{(B C)}^{2}}$ towards BC

Step 2: Find the motion of the mass m.

$(B C) = 2 A B$

$\Rightarrow F = \frac{G M m}{{(2 A B)}^{2}} = \frac{G M m}{4 {(A B)}^{2}} < F_{B A}$

Hence, m will move towards BA (i.e., 2M).

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