The velocities of three particles of masses 20 g- 30 g and 50 g are 10 i- 10 j- and 10 k- respectively- The velocity of the centre of mass of the three particles is A- 2 i-3 j-5 k-B- 10i-j-k-C- 20 i-30 j-5 k-D- 2 i-30 j-50 k-

The correct option is A Velocity of centre of mass v_cm = m_1v_1+m_2v_2+m_3v_3/m_1+m_2+m_3 = 20 × 10i +30 × 10j+ 50 × 10k/100. ...

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Standard XII

Physics

Intuition for COM

The velocitie...

Question

The velocities of three particles of masses 20g, 30g and 50g are $10 \to i, 10 \to j,$ and $10 \to k$ respectively.
The velocity of the centre of mass of the three particles is

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Solution

The correct option is A
Velocity of centre of mass $v_{c m} = \frac{m_{1} v_{1} + m_{2} v_{2} + m_{3} v_{3}}{m_{1} + m_{2} + m_{3}}$
$v_{c m} = \frac{20 \times 10 ˆ i + 30 \times 10 ˆ j + 50 \times 10 ˆ k}{100} = \frac{200 ˆ i + 300 ˆ j + 500 ˆ k}{100}$
$v_{c m} = 2 ˆ i + 3 ˆ j + 5 ˆ k$ .

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The velocities of three particles of masses 20g, 30g and 50g are 10→i,10→j, and 10→k respectively. ​The velocity of the centre of mass of the three particles is

The correct option is A Velocity of centre of mass vcm=m1v1+m2v2+m3v3m1+m2+m3vcm=20×10ˆi+30×10ˆj+50×10ˆk100=200ˆi+300ˆj+500ˆk100vcm=2ˆi+3ˆj+5ˆk.

The velocities of three particles of masses 20g, 30g and 50g are $10 \to i, 10 \to j,$ and $10 \to k$ respectively.
The velocity of the centre of mass of the three particles is

The correct option is A
Velocity of centre of mass $v_{c m} = \frac{m_{1} v_{1} + m_{2} v_{2} + m_{3} v_{3}}{m_{1} + m_{2} + m_{3}}$
$v_{c m} = \frac{20 \times 10 ˆ i + 30 \times 10 ˆ j + 50 \times 10 ˆ k}{100} = \frac{200 ˆ i + 300 ˆ j + 500 ˆ k}{100}$
$v_{c m} = 2 ˆ i + 3 ˆ j + 5 ˆ k$ .