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 replaced by another one made of same meterial but twice the radius, the new elongation is

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

Answer 1

The correct option is C $3.2mm$

$\begin{array}{c}{V}_1=\frac{4}{3}\pi r_1^3⟶\text{mass}=m\text{.}\\ V_2=\frac{4}{3}\pi {\left(2r_1\right)}^3=8V_1⟶\text{mass}=8m\end{array}$

$\begin{array}{cc}\Delta l_1& =\frac{F_{1}l}{AY}=\frac{mgl}{AY}=0.4mm\\ \Delta l_2& =\frac{F_{2}l}{AY}=\frac{8mgl}{AY}=3.2mm.\\ & \text{Ans : (c)}\end{array}$