Problem $1$:

Data taken from a torsion test for a material are given in the table. The curve is linear between the origin and the first point. Plot the diagram, and determine:

$1.$

the torsional modulus of resilience,

$2.$

the torsional modulus of toughness,

$3.$

if Poisson's ratio of the material is known $v=0\mathrm{.}23,$ calculate the modulus of elasticity $E.$