A body A of mass m = 0.1kg has an initial velocity of 3 ^ i m s ^ -...

A body

A

of mass

m = 0.1kg

has an initial velocity of

3\overset{^}{i}m{s}^{- 1}

. It collides elastically with another body

B

of the same mass which has an initial velocity of

5\overset{^}{j}m{s}^{- 1}

. After the collision,

A

moves with a velocity

\overset{\to}{v} = 4\left(\overset{^}{i} + \overset{^}{j}\right)

. The energy of

B

after the collision is written as

\dfrac{x}{10}J

. The value of

x

Correct answer

Step-by-step solution

Using the principle of conservation of linear momentum

$0 . 1 \times 3\overset{^}{i} + 0 . 1 \times 5\overset{^}{j} = 0 . 1 \times 4\left(\overset{^}{i} + \overset{^}{j}\right) + 0 . 1 \times \overset{\to}{v}$

$\overset{\to}{v} = - \overset{^}{i} + \overset{^}{j}$

${K}_{B} = \dfrac{1}{2} \times 0 . 1 \times {v}^{2} = \dfrac{1}{10}J$

$x = 1$

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