Question

Two bodies of masses $1 \,kg$ and $2\, kg$ are connected by a metal wire as shown in figure. A force of $10 \,N$ is applied on the body of mass $2\, kg$. The breaking stress of metal wire is $2 \times 10^{9} \,Nm ^{-2}$. What should be the radius of wire used, if it is not to break

• A. $4 \times 10^{-4} m$
• B. $5 \times 10^{-4}$
• C. $0.23 \times 10^{-4}$
• D. $5.2 \times 10^{-4} m$

Answer 1

Answer: (C)

$T=\frac{m_{2} F}{m_{1}+m_{2}}=\frac{1 \times 10}{3}=\frac{10}{3} N$
$\frac{F}{A}=2 \times 10^{9} \,Nm ^{-2}$
$\frac{10}{3 \times \pi r^{2}}=2 \times 10^{9}$
$\Rightarrow r^{2}=\frac{10^{-8}}{6 \pi}$
$r=\frac{10^{-4}}{\sqrt{6} \pi}=0.23 \times 10^{-4} m$