A lift of mass 2000 kg is supported by thick steel ropes . If maximum upward acceleration of the lift be `1.2 m//s^(2)` , and the breaking stress for the ropes be
`2.8 xx 10^(8) Nm^(-2)`
what should be the minimum diameter of rope ?

Options

A. 10 m
B. `10^(-1) m `
C. `10^(-2)m`
D. `10^(-3)m`

Answer

C

Explanation

Stress `=("Force")/("Area")`
`therefore " Area" = ("Force")/("Stress")=(F)/("Stress")`
`pi r^(2) =(10^(3)xx9.8)/(1.4xx10^(8))=(7xx10^(3))/(10^(8))`
` r^(2)=(7xx10^(-5))/(22) = (49)/(22) xx10^(-5)`
`r^(2)=2.2xx10^(-5)=22xx10^(-6)`
`d= 2r`
`=2sqrt(22)xx10^(-3)`
`=sqrt(4xx22) xx10^(-3) = sqrt(88) xx10^(-3)`
`=9.8xx10^(-3)`
`=10^(-2)m`.