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 `2xx10^9 N m^-2`. What should be the minimum radius of the wire used if it is not to break?

Options

A. `4.6xx10^-5m`
B. `4.6xx10^-6m`
C. `2.5xx10^-6m`
D. `2.5xx10^-5m`

Answer

A

Explanation

Stress in wire `=("Tension")/("Area of cross section")`
T-10=1a …..(1)
20N-T=2a…..(2)
On solving equations (1) and (2), we get,
`T=40/3 N`
Stress,`sigma=(40/3)/(pir^(2)) `
Minimum radius to avoid failure is,
`2xx10^(9) = (40/3)/(pir^(2))`
`therefore r=4.6xx10^(-5)m`