Question

Two bodies of masses $2kg$ and $4kg$ are moving with velocity $2m{s^{ - 1}}$ and $10m{s^{ - 1}}$ towards each other due to mutual gravitational attraction. What is the velocity their centre of mass$?$
A. $5 \cdot 3m{s^{ - 1}}$
B. $6 \cdot 4m{s^{ - 1}}$
C. $zero$
D. $8 \cdot 1m{s^{ - 1}}$

Answer 1

Hint:
Given that the two bodies having mass $2kg$ and $4kg$ moving with velocity $2m{s^{ - 1}}$ and $10m{s^{ - 1}}$ towards each other, we have to find out the velocity of centre of mass for that we have to find out the coordinates of $x$ and $y$ . With help of these we can find the accurate answer.

Complete step by step solution:
Suppose that we have two bodies in which the first body is having $2kg$ and the second body having mass $4kg$ and the first body having velocity $10m{s^{ - 1}}$ . And we have to find out the velocity of centre of mass
We know that,
Velocity of centre of mass $ = \dfrac{{{m_1}{v_1} \times {m_2}{v_2}}}{{{m_1}{m_2}}}$
When bodies are moving towards each other then there will be positive signs in the formula.
So, in the question we know that the bodies are moving due to mutual gravitational attraction which means there is no external force acting on it and if external force is not acting then that means there is no change in centre of mass and if centre of mass is having no change that means there is no change in velocity, So the mass will not change its position.
So, $v_{cm} = 0$
Due to no change in centre of mass. Internal force does not change the position of centre of mass.
So, the accurate answer is zero.
Option (C) is correct.

Note:
For solving this question the step we have to remember is to find out the velocity of two bodies and centre of mass. By putting the formula, we can find. Since, we know that bodies are moving due to mutual gravitational attraction which means there is change in the centre of mass. When there is no change means no motion so the answer will be zero. By doing step by step, we can solve this question.