After a fall, a 90 kg rock climber finds himself dangling from the end of a rope that had been 16 m long and 7.8 mm in diameter but has stretched by 3.1 cm. For the rope, calculate

(a) the strain,
(b) the stress, and
(c) the Young's modulus.

Explanation:

Given that,

Mass of the rock climber, m = 90 kg

Original length of the rock, L = 16 m

Diameter of the rope, d = 7.8 mm

Stretched length of the rope,

(a) The change in length per unit original length is called strain. So,

(b) The force acting per unit area is called stress.

(c) The ratio of stress to the strain is called Young's modulus. So,

Hence, this is the required solution.