\[(a)\;16\;m \quad (b)\;4.8 m\quad (c)\; 8 m \quad (d)\;12.8\;m\]

From work energy theorem

For upward motion

$\large\frac{1}{2}$$m(16)^2=mgh+W$----(1) (Work done against resistance)

For downward motion

$\large\frac{1}{2}$$m(8)^2=mgh-W$ -----(2)

From (1) and (2)

$\large\frac{1}{2} $$ m [(16)^2-8^2]=m2gh$

$\large\frac{1}{2}$$[256-64]=2 \times 10 \times h$

$h=4.8 \;m$

Hence b is the correct answer

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