Question

the length of a wire increased by 8 millimetre when a weight of 5 kg is suspended from it it if other thing will remain same but the radius of the wire is doubled, what will be the increase in its length

Answer 1

Answer:

This question is related to the elastic property of solid matters. Since all the things except the radius of the wire is changed, both cases, before and after increasing the radius, have the same Young's modulus, which is the elasticity coefficient of length of solid matters.

Young's modulus is expressed as,

Y = FL/Al;

Where, F is the force on the wire, here the weight of the 5kg mass, L is the initial length, A is the cross sectional area on which force is exerted & l is the change in length.

So, for the first case we get,

Y = FL/Al

=> l = FL/AY = 8mm

When you double the radius, the cross sectional area increases by a factor of 4, since A~r^2. So, here we get, the area for the second case is four times the area of the first case, i.e. A'=4A.

So here, the increase in length,

l' = FL/A'Y = FL/4AY

Comparing the two expressions we can see length increase in the second case is 1/4 times the length increase with smaller cross sectional area. That is, l' = l/4 = 8mm/4 = 2mm

:

Answer 2

Answer: 2mm

Explanation: EASY!! Youngs modulus before and after remains same for the wire...just use the formula and calculate delta L2

I have attached the answer.