Question

Two blocks of masses $5 \, kg$ and $10 \, kg$ are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal wire is $2\times 10^{9} \, N \, m^{- 2}$ . If $g=10 \, m \, s^{- 2}$ , then what is the minimum radius of the wire which will not break

• A. $\text{0.1} \, mm$
• B. $\text{0.2} \, mm$
• C. $\text{0.05} \, mm$
• D. $\text{0.25} \, mm$

Answer 1

Answer: (A)

This is Atwood's machine. Let the tension in the wire be $T$ and acceleration of masses $a$ .
Then, $T-5g=5a$ and $10g-T=10a$
This gives $a=\frac{1}{3}g$ and $T =\frac{20}{3}\text{g}=\frac{200}{3}\text{N}$ .
Stress $=\frac{ T }{\text { area }}=\frac{200}{3 \times 3.14 \times r ^{2}}=2 \times 10^{9}$ (given)
Thus the minimum radius $r$ should be $r=\sqrt{\frac{200}{3 \times 3 \text{.} 14 \times 2 \times 10^{9}}}=1\text{.}03\times 10^{- 4}m\approx0\text{.}1\text{mm}$