Question

Two objects of masses \( 1\,\text{kg} \) and \( 2\,\text{kg} \) are moving towards each other with accelerations \( 2\,\text{m s}^{-2} \) and \( 3\,\text{m s}^{-2} \) respectively on a smooth horizontal surface. The acceleration of centre of mass of the system is

• A. \( \frac{4}{3}\,\text{m s}^{-2} \) in the direction of acceleration of 2 kg mass
• B. \( \frac{2}{3}\,\text{m s}^{-2} \) in the direction of acceleration of 1 kg mass
• C. \( \frac{2}{3}\,\text{m s}^{-2} \) in the direction of acceleration of 2 kg mass
• D. \( \frac{4}{3}\,\text{m s}^{-2} \) in the direction of acceleration of 1 kg mass
• E. zero

Hint:

Always assign proper sign based on direction before applying formula.

Answer 1

The Correct Option is A

Concept: \[ a_{cm} = \frac{m_1 a_1 + m_2 a_2}{m_1 + m_2} \]

Step 1: Take direction carefully.
Let acceleration of 2 kg mass be positive. \[ a_{cm} = \frac{1(-2) + 2(3)}{3} = \frac{-2 + 6}{3} = \frac{4}{3} \] Direction → towards 2 kg mass.