if a disc slides from top to bottom of an inclined plane ,it takes time t1.If it rolls, it takes time t2 .Now t₂ ²/t₁ ²ⁱs________

Suppose the length of inclined plane is 'l' and it is inclined at an angle '$\mathrm{\theta }$'.
When the disc slides, then the time taken is given by,
$$\begin{gathered} {\mathrm{t}}_1=\sqrt{\frac{2\mathrm{l}}{\mathrm{g} \mathrm{sin\theta }}} \\ {{\mathrm{t}}_1}^2=\frac{2\mathrm{l}}{\mathrm{g} \mathrm{sin\theta }}---\left(\mathrm{i}\right) \\ \mathrm{When} \mathrm{disc} \mathrm{rolls}, \mathrm{then} \mathrm{the} \mathrm{time} \mathrm{taken} \mathrm{is} \mathrm{given} \mathrm{by} \\ {\mathrm{t}}_2=\sqrt{\frac{3 \mathrm{l}}{\mathrm{g} \mathrm{sin\theta }}} \\ {{\mathrm{t}}_2}^2=\frac{3 \mathrm{l}}{\mathrm{g} \mathrm{sin\theta }}---\left(\mathrm{ii}\right) \\ \mathrm{Now}, \\ \frac{{{\mathrm{t}}_2}^2}{{{\mathrm{t}}_1}^2}=\frac{3}{2} \end{gathered}$$