Question

A solid sphere hung at the lower end of a wire is suspended from a fixed point so as to give an elongation of $0.4mm$. When the first solid sphere is replaced by another one made of same material but twice the radius, the new elongation is

• A. $0.8mm$
• B. $1.6mm$
• C. $3.2mm$
• D. $1.2mm$

Answer 1

Answer: (C)

$3.2mm$

As radius is doubled volume becomes 8 times and, hence, the wt. of sphere.
The force becomes 8 times.
$F\propto \Delta L$
$\therefore \Delta L$ also becomes 8 times
$\Delta L^{\prime }=8\times 0.4mm$$=3.2mm$