Two blocks of masses 2 kg and 3kg are connected by a metal wire going over a smoother pulley as shown in figure. The breaking stress of the steel is `2xx10^(9)Nm^(-2)`. What would be the minimum radius of the wire used if it not to break ? Take ,`g=10 ms^(-2)`

Explanation

Equation of motion for 3 kg mass
`30-T=3a" "…(i)`
Equation of motion for 2 kg mass
`T-20=2a" "…(ii)`

From Eqs.(i) and (ii)
`(30-T)/(T-20)=3//2`
`2(30-T)=3(T-20)`
`60-2T=3T-20`
`5T=80impliesT=16N`
Breaking stress, `sigma=(T)/(A)implies2xx10^(9)=(16)/(A)" "(because " stress"=("force")/("area"))`
Area, `A=8xx10^(-9)m^(2)impliespir^(2)=8xx10^(-9)" "(because A=pir^(2))`
Minimum radius of the wire
`r=((8xx10^(-9))/(3.14)_^(1//2)=5xx10^(-5)m`