Calculate the torque N twisting a steel tube of length `l=3.0m` through an angle `varphi=2.0^@` about its axis, if the inside and outside diameters of the tube are equal to `d_1=30mm` and `d_2=50mm`.

Explanation

Clearly `N=underset(d_1//2)overset(d_z//2)int(2pir^3drvarphiG)/(l)=(pi)/(32l)Gvarphi(d_2^4-d_1^4)`
using `G=81GPa=8*1xx10^(10)N/m^2`
`d_2=5xx10^-2m, d_1=3xx10^-2m`
`varphi=2*0^@=(pi)/(90)` radius, `l=3m`
`N=(pixx8*1xxpi)/(32xx3xx90)(625-81)xx10^2N*m`
`=0*5033xx10^3N*m~~0*5k N*m`