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 `2xx10^9m^-2`. What should be the minmum 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 equations of motion of the two blocks are
`T-10N=(1kg)a`
`and 20N-T=(2kg)a`
ElimiN/Ating a from these equations
`T=(40/3)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^-5m`.