A 2 kg body and a 3 kg body are moving along the x-axis. At a particular instant the 2 kg body has a velocity of 3 m/s and ….

Q: A 2 kg body and a 3 kg body are moving along the x-axis. At a particular instant the 2 kg body has a velocity of 3 m/s and the 3 kg body has the velocity of 2 m/s. The velocity of the centre of mass at that instant is

(a) 5 m/s

(b) 1 m/s

(c) 0

(d) None of these

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Ans: (d)
Sol: The velocity of center if mass is

$\displaystyle \vec{v_{cm}} = \frac{m_1 \vec{v_1} + m_2 \vec{v_2}}{m_1 + m_2}$

$\displaystyle \vec{v_{cm}} = \frac{2 \times 3 + 3 \times 2}{2 + 3}$

$\displaystyle v_{cm} = \frac{6 + 6}{5} = \frac{12}{5} m/s$