A spring 20cm long is stretched to 25cm by a load 5N. What will be it's length when stretched by 100N assuming that the elastic limit is not reached?

Answer 1

I remember from my high-school physics classes that the expansion or compression of a spring
is proportional to the force applied to it. That is, it is linears (within obvious restrictions)
A good example of this is a simple fisherman's scale. The "ruler" on it is a linear scale, but trying to weigh a shark with it, would probably not give you a correct reading and would break it.

so ..
Stretch = kN, where N is the force applies in Newtons
When N = 5, Stretch = 5 cm
5 = k(5) ---> k = 1 and
Stretch = N
when N = 100, Stretch = 100 cm
and at rest it is 20cm, so it is 120 cm long.

Look at Sal Khan's simplified video:
https://www.khanacademy.org/science/ap-physics-1/ap-work-and-energy/spring-potential-energy-and-hookes-law-ap/v/intro-to-springs-and-hooke-s-law

Answer 2

Load is now 20x, so stretch will be 20x, or 5cm*20=100cm
length now of spring is 100+20 = 120cm

Answer 3

Answer is 30cm
Use young modulus law