Question

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

• A. $2.3\times {10}^{-5}m$
• B. $4.6\times {10}^{-4}m$
• C. $4.6\times {10}^{-5}m$
• D. $2.3\times {10}^{-4}m$

Answer 1

The correct option is C

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

The stress in the wire = $\frac{Tension}{Areaofcrosssection}$
To avoid breaking, this stress should not exceed the breaking stress.
Let the tension in the wire be T. The equations of motion of the two blocks are,
T - 10 N = (1 kg)a
And 20 N - T = (2kg) a.
Eliminating a from these equations,
$T=\left(\frac{40}{3}\right)N$

The breaking stress = $\frac{T}{\pi r^2}$

If the minimum radius needed to avoid breaking is r,

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