Question

A cylinder of length 1.5 m and diameter 4 cm is fixed at one end. A tangential force of 4 × 10⁵ N is applied at the other end. If the rigidity modulus of the cylinder is 6 × 10¹⁰ Nm^-2 then, calculate the twist produced in the cylinder.

Answer 1

Torsion of a cylinder τ = `(πη"r"^4Φ)/(2"l")`

Twist produced in the cylinder Φ = `(τ xx (2"l"))/(πη"r"^4) = (("F" xx "l") xx (2"l"))/(πη"r"^4)`

= `(4 xx 10^5 xx 2 xx (1.5)^2)/(3.14 xx 6 xx 10^10 xx (2 xx 10^-2)4)`

= `(18 xx 10^5)/(3.01 xx 10^-6 xx 10^10)`

Φ = 59.80