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Law of Conservation of Mechanical Energy

Consider two ...

Question

Consider two perfectly elastic spheres having velocities $u_{1}$ and $u_{2}$ in the same direction and masses $m$ and $m^{'}$ . When these two spheres collide, the impulse of the blow on the spheres is

A

\frac{2 m m^{1}}{m + m^{1}} (u_{1} - u_{_{2}})

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B

\frac{2 m m^{1}}{m - m^{1}} (u_{1} - u_{_{2}})

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C

\frac{2 m m^{1}}{m + m^{1}} (u_{1} + u_{_{2}})

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D

\frac{2 m m^{1}}{m - m^{1}} (u_{1} + u_{_{2}})

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Solution

The correct option is D $\frac{2 m m^{1}}{m + m^{1}} (u_{1} - u_{_{2}})$
Momentum conservation,
$m_{1} u_{1} + m_{2} μ_{2} = m_{1} v_{1} + m_{2} v_{2}$ .........(2)

& $e = \frac{v_{2} - v_{1}}{u_{1} - u_{2}}$

$v_{2} - v_{1} = u_{1} - μ_{2}$ ...........(1)
Put (1) in (2)

$\Rightarrow I m p u l s e = \frac{2 m m^{'}}{m + m^{'}} (u_{1} - u_{2})$

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