Question

Young's modulus for aluminium is 7 × 10¹⁰ Pa. The force needed to stretch an aluminium wire of diameter 2 mm and length 800 mm by 1 mm is ______.

पर्याय

• 2.75 newton

• 275 newton

• 1.10 newton

• 275 k newton

Answer 1

Young's modulus for aluminium is 7 × 10¹⁰ Pa. The force needed to stretch an aluminium wire of diameter 2 mm and length 800 mm by 1 mm is 275 newton.

Explanation:

Given, Young's modulus for aluminium, Y = 7 × 10¹⁰ pa

Diameter of aluminium wire, d = 2 mm 2mm

Radius of aluminium wire, r = `(2 "mm")/2` = 1 mm

Length of aluminium wire, I = 800 mm

Increase in length of aluminium wire, Δl = 1 mm

Young's modulus, Y = `("F"/"A")/((Deltal)/l)`

`= ("F" xx l)/("A" xx Delta l)`

`= (7 xx 10^10) = ("F" xx 800 xx 10^-3)/(pi xx 1 xx 10^-6 xx 1 xx 10^-3)`

`=> "F" = (7 xx 10^10 xx 3.14 xx 10^-9)/(800 xx 10^-3)`

`= (21.98 xx 10)/(8 xx 10^-1)`

= 2.75 × 10²

= 275 N