d
\(\text { Velocity just before collision }=\sqrt{2 \mathrm{gh}}\)

\(\text { Velocity just after collision }=\sqrt{2 \mathrm{~g}\left(\frac{\mathrm{h}}{2}\right)}\)

\(\therefore \Delta \mathrm{KE}=\frac{1}{2} \mathrm{~m}(2 \mathrm{gh})-\frac{1}{2} \mathrm{mgh}\)

\(=\frac{1}{2} \mathrm{mgh}\)

\(\therefore \% \text { loss in energy }\)

\(=\frac{\Delta \mathrm{KE}}{\mathrm{KE}_{\mathrm{i}}} \times 100=\frac{\frac{1}{2} \mathrm{mgh}}{\frac{1}{2} \mathrm{mg} 2 \mathrm{~h}} \times 100=50 \%\)

Hence option \((4)\)