Question

Q6. If Young’s modulus of steel is 2.0X1011 N/m2

, then how much weight should be suspended

from a steel wire of length 2.0 m and diameter 1.0 mm so that the length of wire be increased

by 1.0 mm.​

Answer 1

Given,

Young's modulus of steel = 2 × 10^11 Nm^-2

= 2 × 10^5 N mm^-2

length of steel wire = 2 m = 2000 mm

extension in wire = 1 mm

diameter of wire = 1 mm

So, radius of wire = 0.5 mm

area of cross section of wire = πr^2 = 0.25 mm^2

We know,

F/A = Y∆l/l

where F is force acting on body

A is area of cross section of wire

Y is Young's modulus

∆l is extension of wire

l is length of wire

F = mass × acceleration

Here acceleration is due to gravity.

So, F = mg

Taking g = 10 ms^-2 = 1000 mm s^-2

(m× 1000)/0.25 = (2 × 10^5 × 1)/2000

2 × 10^6 × m = 5 × 10^4

m = 5/200 = 0.025 kg = 25 g

25 g should be suspended.