Two object of masses 200 g and 500 g possess velocities 10i m/s and ( 3i + 5j ) m/s respectively. The velocity of their centre of mass in m/s is

Q: Two object of masses 200 g and 500 g possess velocities 10 i m/s and ( 3i + 5j ) m/s respectively. The velocity of their centre of mass in m/s is

(a) 5i – 25j

(b) 7/5 i – 25j

(c) 5i + 25/7 j

(d) 25i – 5/7 j

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Ans: (c)
Sol: $\displaystyle \vec{v_{cm}} = \frac{m_1 \vec{v_1} + m_2 \vec{v_2}}{m_1 + m_2}$

$\displaystyle \vec{v_{cm}} = \frac{200 \times 10 \hat{i} + 500 \times (3 \hat{i}+ 5 \hat{j})}{200 + 500}$

$\displaystyle \vec{v_{cm}} = \frac{20 \hat{i} + 5 (3 \hat{i}+ 5 \hat{j})}{7}$

$\displaystyle \vec{v_{cm}} = \frac{35 \hat{i} + 25 \hat{j}}{7}$

$\displaystyle \vec{v_{cm}} = 5 \hat{i} + \frac{25}{7}\hat{j} $