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 `(40//3pi)xx10^(6)N//m^(2)`. If `g=10ms^(-2)`, then what should be the minimum radius of the wire used if it is not to break?

Options

A. `0.5mm`
B. `1mm`
C. `1.5mm`
D. `2mm`

Answer

B

Explanation

`T=(2m_1m_2)/(m_1+m_2)g=(2xx1xx2)/(1+2)xx10N=(40)/(3)N`
If `r` is the minimum radius, then
breaking stress`=((40)/(3))/(pir^2)` or `(40)/(3pi)xx10^6=(40)/(3pir^2)`
or `r^2=(1)/(10^6)` or `r=(1)/(10^3)m`
or `r=(1)/(10^3)xx10^3m=1mm`