You hang a heavy ball with a mass of 10 kg from a gold wire 2.6 m long that is 1.6 mm in diameter. You measure the stretch of the wire, and find that the wire stretched 1.99 mm. Calculate Young’s modulus for the wire. [Use g = 9.81 m/s2]

The Young's modulus for the wire is

Explanation:

Young's Modulus is defined as the ratio of stress acting on a substance to the amount of strain produced.

The equation representing Young's Modulus is:

where,

Y = Young's Modulus

F = force exerted by the weight  =

m = mass of the ball = 10 kg

g = acceleration due to gravity =

l = length of wire  = 2.6 m

A = area of cross section  =

r = radius of the wire =      (Conversion factor:  1 m = 1000 mm)

= change in length  = 1.99 mm =

Putting values in above equation, we get:

Hence, the Young's modulus for the wire is

where are the vectors ?