Question

Two bodies of 2 Kg & 4 Kg are moving with velocities 20 m/s and 10 m/s respectively towards each other under mutual gravitational attraction. Find the velocity of their centre of mass in m/s.
1. 5
2. 6
3. 8
4. Zero
5.

Answer 1

Correct Answer - Option 4 : Zero

Concept:

position of the centre of mass:

\({x_{cm}} = \frac{{{m_1}{x_1} + {m_2}{x_2} + \ldots + {m_n}{x_n}}}{{{m_1} + {m_2} + \ldots + {m_n}}}\)

The velocity of the centre of mass:

\({V_{cm}} = \frac{{{m_1}{v_1} + {m_2}{v_2} + \ldots + {m_n}{v_n}}}{{{m_1} + {m_2} + \ldots + {m_n}}}\)

Acceleration of the centre of mass:

\({a_{cm}} = \frac{{{m_1}{a_1} + {m_2}{a_2} + \ldots + {m_n}{a_n}}}{{{m_1} + {m_2} + \ldots + {m_n}}}\)

Calculations:

\({\vec V_{cm}} = \frac{{{m_1}{v_1} + {m_2}{v_2}}}{{{m_1} + {m_2}}}\)

\(= \frac{{2 \times 20 - 4 \times 10}}{{2 + 4}}\)  (Negative because both are moving in the opposite direction)

= 0