First slide

In the frame of centre of mass

Question

Two particles A and B having masses m and 3m are initially at rest at a separation 4m. They start moving towards each other under the influence of mutual gravitational force of attraction. After some time, if displacement of A is 0.1 m, then magnitude of displacement of B at that instant is

Moderate

A

1 m
B

$\frac{1}{3} m$
C

$\frac{1}{6} m$
D

$\frac{2}{3} m$

Solution

(2)
As external force acting on the system is zero, position of its centre of mass remains unchanged.
$\begin{array}{l} ∴ (m_{A} + m_{B}) \times r_{c m} = m_{A} . r_{A} + m_{B} . r_{B} \\ \Rightarrow (m_{A} + m_{B}) \times Δ r_{c m} = m_{A} . Δ r_{A} + m_{B} . Δ r_{B} \\ \Rightarrow (m + 3 m) \times 0 = m \times 1 + 3 m \times Δ r_{B} \\ \Rightarrow Δ r_{B} = - \frac{1}{3} m e t r e . \end{array}$
Therefore B moves by 1/3 metre in opposite direction.

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