A bob of mass m , suspended by a string of length l _ 1 , is given...

As shown in the figure shown above, the minimum speed required by the bob of mass $m$ attached to the string of length ${l}_{1}$ in order to complete the full circle is $\sqrt{5g{l}_{1}}$.

When the bob goes to the highest point, its speed becomes $\sqrt{g{l}_{1}}$. Here, it strikes with the identical mass, which is tied to the string of length ${l}_{2}$. The speed delivered to the object is $\sqrt{g{l}_{1}}$. This should be equal to $\sqrt{5g{l}_{2}}$ so that this bob could complete a full circle.
$\sqrt{g{l}_{1}} = \sqrt{5g{l}_{2}}$
$⇒ g{l}_{1} = 5g{l}_{2}$
$⇒ \dfrac{{l}_{1}}{{l}_{2}} = 5$