Question

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

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

Answer 1

The correct option is B $1.6$ mm

$\begin{array}{c}\text{case}1\to m_1=\rho V_1=\rho 4\pi r^2\\ \text{case}2\to m_2=\rho V_2=\rho 4\pi (2r{)}^2=4\left(\rho 4{\pi }^2\right)=4m_1\end{array}$

$\begin{array}{c}\frac{F}{A}=Y\frac{\Delta l}{l}\\ \Rightarrow \Delta l_1=\frac{Fl}{AY}=\frac{m_{1}gl}{AY}=0.4mm\\ \text{But}\\ \Delta l_2=\frac{m_{2}gl}{AY}=\frac{4m_{1}gl}{AY}=4\times 0\cdot 4mm=1.6mm\\ \text{Answer is}\left(B\right)\end{array}$