Question

A wire of length '$l$' and radius '$r$' is clamped rigidly at one end. When the other end of the wire is pulled by a force '$F$', its length increases by ${}^{\prime }{x}^{\prime }$. Another wire of same material of length '$2l$' and radius ${}^{\prime }2r$' is pulled by a force '$2F^{\prime }$, the increase in its length will be :

• A. $x$
• B. $2x$
• C. $x/2$
• D. $4x$

Answer 1

The correct option is A $x$

In the first case we have
$x=\frac{Fl}{\pi r^{2}Y}$
and in the for the second wire we have the change in length as
$\frac{2F\times 2l}{\pi (2r{)}^{2}Y}=\frac{Fl}{\pi r^{2}Y}=x$