Two identical balls each of mass 4 kg are moving towards each other with speeds 2 m/s and 3 m/s respectively, they undergo head on perfectly elastic collision. the impulse imparted by one ball on other is:

12 Ns

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8 Ns

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20 Ns

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40 Ns

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Solution

The correct option is C 20 Ns
Applying conservation of linear momentum in $x$ direction
$u_{1} = 2$ and $u_{2} = 3$ (in $- x$ direction)

initial momentum $= m 2 - m 3$
final momentum $= m v_{2} - m v_{1}$
equating both
$- m = m v_{2} - m v_{1}$
$⟹ v_{2} - v_{1} = - 1$ .............. $e q (1)$

from definition of coeficient of restitution which states that

velocity of separation $= e \times$ (velocity of approach)
$⟹ v_{2} - (- v_{1}) = u_{1} - (- u_{2})$

$v_{2} + v_{1} = 2 + 3 = 5$ ............... $e q (2)$

solving $e q (1)$ and $e q (2),$ we get

$v_{1} = 3$ and $v_{2} = 2$

considering ball $B$

$J (i m p u l s e) = m v_{2} - m (- u_{2}) = m (v_{2} + u_{2}) = 4 (2 + 3)$

$J = 20 N - s$

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