The ratio of times taken by freely falling body to cover first metre, second metre, …. is

If ${\text{h}}_{\text{1}}=1{\text{m,t}}_{\text{1}}=\sqrt{1}=1$

${\text{h}}_{\text{2}}=2{\text{m,t}}_{\text{2}}=\sqrt{2}$

${\text{h}}_{\text{3}}=3{\text{m,t}}_{\text{3}}=\sqrt{3}$

For 2^nd meter journey, ${\text{t}}_2-{\text{t}}_{\text{1}}=\sqrt{2}-1$

For 3^rd meter journey, ${\text{t}}_3-{\text{t}}_{\text{2}}=\sqrt{3}-\sqrt{2}$

$\therefore {\text{t}}_{\text{1}}:\left({\text{t}}_{\text{2}}-{\text{t}}_{\text{1}}\right):\left({\text{t}}_{\text{3}}-{\text{t}}_{\text{2}}\right)=1:\left(\sqrt{2}-1\right):\left(\sqrt{3}-\sqrt{2}\right)$