Question

Two blocks of masses $1\text{kg}$ and $2\text{kg}$ are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal is $\left(10/3\pi \right)\times {10}^6{\text{N/m}}^2$. If $g=10{\text{m/s}}^2$, then what should be the minimum radius of the wire used if it is not to break?

• A. $0.5\text{mm}$
• B. $1.5\text{mm}$
• C. $1\text{mm}$
• D. $2\text{mm}$

Answer 1

The correct option is D $2\text{mm}$

Tension in the string, $T=\frac{2m_1{m}_2}{m_1+m_2}g=\frac{2\times 1\times 2}{1+2}\times 10=\frac{40}{3}\text{N}$
If $r$ is the minimum radius, then
Breaking stress $=\frac{40/3}{\pi r^2}$
$\frac{10}{3\pi }\times {10}^6=\frac{40}{3\pi r^2}$
$r^2=\frac{4}{{10}^6}$
$r=\frac{2}{{10}^3}\text{m}=2\text{mm}$