$m$ -mass of $1st$ body, $M$ -Mass of the Initial kinetic energy of system

$K_i=\large\frac{1}{2}$$mu^2+\large\frac{1}{2}$$M(0)^2$

$\qquad=\large\frac{1}{2} $$ \times 0.5 \times 2^2$

$\qquad=1 J$

For collision applying conservation of linear momentum

$mu=(M+m)v$

$0.5 \times 2=(0.5 +1)v$

$v=\large\frac{2}{3}$$ m/s$

Finally Kinetic energy

$K_f=\large\frac{1}{2}$$(0.5+1) \times \large\frac{2}{3} \times \frac{2}{3}$

$\qquad=\large\frac{1}{3}\;$$J$

Energy lost $=1-\large\frac{1}{3}=\frac{2}{3}$$=0.67 \;J$

Hence a is the correct answer.

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