Two bodies A and B of same mass are placed at position r A -2 -k- and r B -2 -2 k- respectively- If the bodies are displaced from their initial position to r A -2 -4 -k- and r B -3 -4 -2 k- find the magnitude of displacement of COM of the system-A- -18 unitsB- -16 unitsC- -16 unitsD- -10 units

The correct option is D √(10) unitsDisplacement of COM, Δr_com = m_A Δr_A + m_B Δr_Bm_A + m_B Δr_A = r_A' r_A nbsp; = (2î + 4ĵ + k̂) (î + 2ĵ + k̂) Δr_A = (î ...

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Byju's Answer

Standard XII

Physics

Displacement of COM:Application

Two bodies A ...

Question

Two bodies $A$ and $B$ of same mass are placed at position ${\to r}_{A} =^i + 2^j +^k$ and ${\to r}_{B} = 2^i + 2^k$ respectively. If the bodies are displaced from their initial position to ${\to r}_{A^{'}} = 2^i + 4^j +^k$ and ${\to r}_{B^{'}} = 3^i + 4^j + 2^k$ , find the magnitude of displacement of COM of the system.

- \sqrt{18}

units

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- \sqrt{16}

units

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\sqrt{16}

units

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\sqrt{10}

units

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Solution

The correct option is D $\sqrt{10}$ units
Displacement of COM, $Δ {\to r}_{c o m} = \frac{m_{A} Δ {\to r}_{A} + m_{B} Δ {\to r}_{B}}{m_{A} + m_{B}}$
$Δ {\to r}_{A} = {\to r}_{A^{'}} - {\to r}_{A} = (2^i + 4^j +^k) - (^i + 2^j +^k)$
$⟹ Δ {\to r}_{A} = (^i + 2^j)$
and
$Δ {\to r}_{B} = {\to r}_{B^{'}} - {\to r}_{B} = (3^i + 4^j + 2^k) - (2^i + 2^k)$
$⟹ Δ {\to r}_{B} = (^i + 4^j)$
Let $m_{A} = m_{B} = m$
$Δ {\to r}_{c o m} = \frac{m . (^i + 2^j) + m (^i + 4^j)}{m + m}$
$= \frac{m}{2 m} (2^i + 6^j)$
$⟹ Δ {\to r}_{c o m} =^i + 3^j$
$| Δ {\to r}_{c o m} | = \sqrt{1^{2} + 3^{2}} = \sqrt{10}$ units

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Two bodies A and B of same mass are placed at position →rA=^i+2^j+^k and →rB=2^i+2^k respectively. If the bodies are displaced from their initial position to →rA′=2^i+4^j+^k and →rB′=3^i+4^j+2^k, find the magnitude of displacement of COM of the system.