Question

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?

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

Answer 1

Correct Answer - B
`T = (2m_(1)m_(2))/(m_(1)+m_(2)) g = (2xx1xx2)/(1+2) xx 10 N = (40)/(3)N`
If r is the minimum radius, then
Breaking stress `= ((40)/(3))/((pir^(2))) or (40)/(3pi) xx 10^(6) = (40)/(3pir^(2))`
or ` r^(2) = (1)/(10^(6)) or r = (1)/(10^(3))m = 1 mm`