Question

Two blocks of masses $3kg$ and $5kg$ are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{24}{\pi }\times 10^{2}N{m}^{-2}$. What is the minimum radius of the wire?
$($ Take $g=10m{s}^{-2})$

• A. 125 cm
• B. 1250 cm
• C. 12.5 cm
• D. 1.25 cm

Answer 1

Answer: (C)

$T=\frac{2m_1{m}_{2}g}{m_1+m_2}$
$=\frac{2\times 3\times 5\times 10}{8}$
$=\frac{75}{2}$
Stress $=\frac{T}{A}$
$\frac{24}{\pi }\times 10^2=\frac{75}{2\times \pi R^2}$
$R^2=\frac{75}{2\times 24\times 100}=\frac{3}{8\times 24}$
$\Rightarrow R=0.125m$
$R=12.5cm$