Question

Two blocks of masses 1 kg and 2 kg are connected by a metal wire of breaking stress $2\times 10^{9} \, N m^{- 2}$ going over a smooth pulley as shown in figure. The minimum radius of the wire required to move without breaking is... (Take $g=10 \, m s^{- 2}$ ; stress = force/Area)

• A. $4.6\times 10^{- 5} \, m$
• B. $4.6\times 10^{- 6 \, }m$
• C. $2.5\times 10^{- 6} \, m$
• D. $2.5\times 10^{- 5} \, m$

Answer 1

Answer: (A)

Let the tension in the wire be T . The equations of motion of the two locks are,
$T-10=1 \, a$
$and \, \, 20-T=2 \, a$
Eliminating $a$ form these equations,
$T=\left(\frac{40}{3}\right)N$
$Stress, \, =\frac{\left(\frac{40}{3}\right)}{\pi \, r^{2}}$
If the minimum radius needed to avoid breakings is $r.$
$2\times \left(10\right)^{9}=\frac{\left(\frac{40}{3}\right)}{\pi \, \, r^{2}}$
Solving this,
$r=4.6\times 10^{- 5} \, m$