A uniform wire of resistance $50\Omega$  is cut into five equal parts. These parts are now connected in parallel. Then the equivalent resistance of the combination is :

We know that resistance is directly proportional to the length of the resistor. Therefore, if the wire is cut into 5 equal parts then the resistance of the wire will also get divided equally:

$\begin{array}{r}{\mathrm{R}}_1={\mathrm{R}}_2={\mathrm{R}}_3={\mathrm{R}}_4={\mathrm{R}}_5\end{array}= 10\mathrm{\Omega }$

When these resistances are connected in parallel, the equivalent resistance can be given by:
$\begin{array}{r}\frac{1}{{\mathrm{R}}_{\text{eq }}}=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}=\frac{5}{10}=\frac{1}{2}\\ \end{array}$
$\therefore {\mathrm{R}}_{\text{eq }}=2\mathrm{\Omega }$