A body A, of mass m = 0.1kg has an initial velocity of 3i^ ms−1. It collides elastically with another body, B of the same mass which an initial velocity of 5j^ms−1. After collision, A moves with a velocity v→=4(i^+j^). The energy of B after collision is written as x10J. The value of x is ________.

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A body A, of mass m = 0.1kg has an initial velocity of $3 \hat{i} {ms}^{- 1}$ . It collides elastically with another body, B of the same mass which an initial velocity of $5 \hat{j} {ms}^{- 1}$ . After collision, A moves with a velocity $\vec{v} = 4 (\hat{i} + \hat{j})$ . The energy of B after collision is written as $\frac{x}{10} J$ . The value of x is ________.

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Detailed Solution

$Initial momentum : \vec{p_{1}} = m 3 \hat{i} + m 5 \hat{j}$

$final momentum \vec{p_{2}} = m 4 (\hat{i} + \hat{j}) + m \vec{v} where \vec{v} is the velocity of the second body after collision$

$By applying the conservation of linear momentum m 3 \hat{i} + m 5 \hat{j} = m 4 (\hat{i} + \hat{j}) + m \vec{v}$

$\vec{v} = - \hat{i} + \hat{j}$

$kinetic energy = \frac{1}{2} (0.1) (2) = 0.1 J = \frac{x}{10} = \frac{1}{10} so x = 1$

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