$w_g+w_B+w_v+w_{\text {ext }}=0$

$mgd -\rho_{ w } \cdot v \cdot g d-6 \pi \eta rvd + w _{\text {ext }}=0$

$\quad \text { (slowly } v =0 \text { ) }$

$w _{\text {ext }}=\rho_{ w } vgd - mgd =\left(1000 \times \frac{4}{3} \times \frac{22}{7} \times\left(\frac{3}{2} \times 10^{-2}\right)^3-\frac{22}{7} \times 10^{-3}\right) gd$

$w _{\text {ext }}=\frac{22}{7} \times 10^{-3}\left[\frac{9}{2}-1\right] \times 10 \times 0.7=\frac{22}{7} \times 10^{-3} \times \frac{7}{2} \times 7$

$w _{\text {ext }}=77 \times 10^{-3} J =0.077 J$

$\text { (B) } wg _{ g }+ w _{ B }= k _{ f }- k _{ i } \quad\left( k _{ i }=0\right)$

$\frac{1}{2} \times \frac{22}{7} \times 10^{-3} v ^2=77 \times 10^{-3}$

$v ^2=\frac{77 \times 7 \times 2}{22}$

$v =7 m / s$

$(C)$ $H =\frac{ v ^2}{2 g }=\frac{49}{20}=2.45 m$