Two bodies of mass 1 kg and 3 kg have positive vectors i + 2j + k and -3i -2j + k respectively. The centre of mass of this system has a position vector:

Options

(a) -2i – j + k
(b) 2i – j – 2k
(c) -i + j + k
(d) -2i + 2k

Correct Answer:

-2i – j + k

Explanation:

The position vector of othe centre of mass of two particle system is given by
R⃗ = m₁R⃗₁ + m₂R⃗₂ / (m₁ + m₂)
= 1/4 [-8i -4j + 4k] = -2i -j + k