Question

Two blocks of masses $1kg$ and $2kg$ are connected by a metal wire going over a smooth pulley. The breaking stress of metal is $\frac{40}{3\pi }\times {10}^6{Nm}^{-2}$. What should be the minimum radius of wire used if it should not break?
($g=10{ms}^{-2}$)

• A. $0.5mm$
• B. $1mm$
• C. $1.5mm$
• D. $2mm$

Answer 1

Answer: (B)

$1mm$

$T=\frac{2m_1{m}_2}{m_1+m_2}g$

$=\frac{2\times 1\times 2}{1+2}\times 10N$

$=\frac{40}{3}N$

If $r$ is the minimum radius, then breaking stress $=\frac{\frac{40}{3}}{\pi r^2}$

$\Rightarrow$$\frac{40}{3\pi r^2}=\frac{40}{3\pi }\times {10}^6$

$\Rightarrow r^2=\frac{1}{{10}^6}$ or $r=\frac{1}{{10}^3}m$

$\Rightarrow r=\frac{1}{{10}^3}\times {10}^{3}mm=1mm$