Question

A steel wire is 1 m long and 1mm^2 in area of cross-section. If it takes 200N to stretch its wire by 1 mm, how much force will be required to stretch a wire of the same material as well as diameter from its normal length of 10 m to a length of 1002 cm?

Answer 1

The force required will be 400 N

Explanation :

In the first case

Length L = 1 m

Area A = 1 mm² = 10⁻⁶ m²

Force F = 200 N

Change in length , L' = 1 mm = 10⁻³ m

we know that young's modulus is given by

Y = FL/AL'

= 200 x 1/(10⁻⁶ x 10⁻³)

= 2 x 10¹¹

Similarly in the second case,

L = 10 m

Area A = 1 mm² = 10⁻⁶ m²

New length = 1002 cm = 10.02 m

Change in length , L' = 10.02 - 10 = 0.02 m = 2 x 10⁻² m

Hence,

Y = FL/AL'

=> F = YAL'/L

= (2 x 10¹¹ x 10⁻⁶ x 2 x 10⁻²)/10

= 400 N

Hence the force required will be 400 N

Answer 2

Answer:

400N

Explanation:

See the attachment