Question

a force of 1000 Newton causing an increase of 0.1% in length of wire of area of cross section 10 raise to power minus 6 m per second square calculate the young modulus of the material of the wire

Answer 1

The Young's modulus of the material of the wire is 10¹².

The force acting upon the material is (F) = 1000 N

The increase in length is (l) = 0.1%

If the actual length is L, the value of l/L = 0.1/100

                                                                = 1/1000

∴ L/l = 1000

The rate of increase in cross section (ΔA) = 10⁻⁶ m²/s

∴ In 1 s, the increase in area of cross section is (A) = 10⁻⁶ m²/s

The Young's modulus,

Y = FL/Al

∴ Y = 1000 × 1000/ 10⁻⁶

⇒ Y = 10¹²

As Y is the ratio of two similar physical units, Y is unit less physical quantity.

So, the value of Young's modulus of the metal is 10¹².