Question

Two blocks of masses $1kg$ and $2kg$ are connected by a metal wire, going over a smooth pulley as shown in the figure. The breaking stress of the metal is $2\times {10}^{9}Nm{s}^{-2}$.What should be the minimum radius of the wire used minimum radius of the wire used so that it should not break? $(Takeg=10m{s}^{-2})$.

• A. $2.3\times {10}^{-5}m$
• B. $4.6\times {10}^{-5}m$
• C. $6.9\times {10}^{-5}m$
• D. $9.2\times {10}^{-5}m$

Answer 1

The correct option is B $4.6\times {10}^{-5}m$

$20-T=2a$

$T-10=a$

$a=\frac{10}{3}$

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

$\frac{F}{A}=\frac{T}{A}=2\times {10}^9$

$\frac{40}{3}=2\times {10}^9\times \pi \times r^2$

$r^2=\frac{2}{3\pi }\times {10}^{-8}$

$r=4.6\times {10}^{-5}m$

Correct option is $\left(B\right)$