Two blocks of masses 1 kg and 2kg are connect by a metal wire going over a smooth pulley as shown in figure. The breaking stress of the metal is `2xx10^9Nm^-2`. What should be the minimum radius of the wire used if it is not to break? Take `g=10ms^-2`

Explanation

The stress in the wire `=("Tension")/("Area of cross-section")`. To avoid breaking, this stress should not exceed the breaking stress.
Let the tension in the wire be `T`. The equation of motion of the two blocks are,
`T=10N=(1 kg )a`
and `20N-T=(2kg)a`.
Eliminating a from these equations,
`T=(40xx3)N`
The stress `=((40//3)N)/(pir^(2))`
If the minimum radius needed to avoid breaking is `r`.
`2xx10^(9)(N)/(m^(2))=((40//3)N)/(pir^(2))`
Solving this, `r=4.6xx10^(-5)m`.