Two particles of masses 3 kg and 2 kg are moving the velocities V 1-2 - and V 2-3 - respectively- The first particle of mass 3 kg has an acceleration of a-1-2 -2 - while acceleration of the second particle is zero- The centre of mass of these two particles follow aA- Circular pathB- Straight line pathC- Elliptical pathD- Parabolic path

The correct option is B Straight line pathV⃗_cm=m_1V⃗_1+m_2V⃗_2/m_1+m_2=6î+5ĵ/5 a⃗_cm=m_1a_1+m_2a_2/m_1+m_2=6î+6ĵ/5 As V⃗_cm||a⃗_cm, so centre of mass follows ...

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Standard XII

Physics

Intuition for COM

Two particles...

Question

Two particles of masses 3kg and 2kg are moving the velocities ${\to V}_{1} = 2^i$ and ${\to V}_{2} = 3^j$ , respectively. The first particle of mass 3kg has an acceleration of ${\to a}_{1} = 2^i + 2^j$ while acceleration of the second particle is zero. The centre of mass of these two particles follow a

Parabolic path

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Circular path

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Straight line path

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Elliptical path

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Solution

The correct option is C Straight line path
${\to V}_{c m} = \frac{m_{1} {\to V}_{1} + m_{2} {\to V}_{2}}{m_{1} + m_{2}} = \frac{6^i + 5^j}{5}$
${\to a}_{c m} = \frac{m_{1} a_{1} + m_{2} a_{2}}{m_{1} + m_{2}} = \frac{6^i + 6^j}{5}$
As ${\to V}_{c m} | | {\to a}_{c m}$ , so centre of mass follows a straight line path.

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Two particles of masses 3kg and 2kg are moving the velocities →V1=2^i and →V2=3^j , respectively. The first particle of mass 3kg has an acceleration of →a1=2^i+2^j while acceleration of the second particle is zero. The centre of mass of these two particles follow a

The correct option is C Straight line path→Vcm=m1→V1+m2→V2m1+m2=6^i+5^j5 →acm=m1a1+m2a2m1+m2=6^i+6^j5 As →Vcm||→acm, so centre of mass follows a straight line path.