\[(a)\;5.0 \times 10^{-12}\;J \quad (b)\;2.25 \times 10^{-10}\;J \quad (c)\;4.0 \times 10^{-11}\;J \quad (d)\;6.0 \times 10^{-15}\;J \]

Work done= Final gravitational potential -Initial gravitational potential

$\qquad=v_f -v_i =3\bigg[\bigg(\large\frac{-Gmm}{r_f}\bigg)-\bigg(\frac{-Gmm}{r_i}\bigg)\bigg]$

$ m= 0.1 \quad r_f=0.4\;m \quad r_i=0.2\; m$

Substituting these values we get

$W= 3\bigg[-Gmm \bigg(\large\frac{1}{.4}-\frac{1}{.2}\bigg)\bigg]$

$W= 5.0 \times 10^{-12}J$

Hence a is the correct answer.

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