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Standard XII

Physics

Velocity of COM

If one dimens...

Question

If one dimensional elastic collision between a given incoming body A of mass $m_{1}$ and another body B of mass $m_{2}$ initially at rest.

B will recoil with greatest speed if

m_{2} << m_{1}

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B will recoil with greatest momentum if

m_{2} >> m_{1}

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B will recoil with greatest kinetic energy if

m_{1} = m_{2}

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B will recoil with greatest kinetic energy if

m_{2} = m_{1}

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Solution

The correct option is C B will recoil with greatest speed if $m_{2} << m_{1}$
Applying the conservation of Momentum
$m_{1} v_{1} + m_{2} \times 0 = m_{1} v_{1}^{^{'}} + m_{2} v_{2}^{^{'}}$
$m_{1} (v_{1} - v_{1}^{^{'}}) = m_{2} v_{2}$
$v_{2} = \frac{m_{1} (v_{1} - v_{1}^{^{'}})}{m_{2}}$
maximum speed can be achieved only if B is very small compared to A

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If one dimensional elastic collision between a given incoming body A of mass m1 and another body B of mass m2 initially at rest.

The correct option is C B will recoil with greatest speed if m2<<m1Applying the conservation of Momentumm1v1+m2×0=m1v′1+m2v′2m1(v1−v′1)=m2v2v2=m1(v1−v′1)m2 maximum speed can be achieved only if B is very small compared to A

If one dimensional elastic collision between a given incoming body A of mass $m_{1}$ and another body B of mass $m_{2}$ initially at rest.