Physics Spring problem?!

The two massless springs have the same length L0 when not compressed or stretched. The stiffness of each spring is k1 and k2, respectively. Mass M1 hangs from spring 1 and it reaches equilibrium at position L1. Mass M2 hangs from spring 2 and it reaches equilibrium at position L2.


If k2 = k1 and M2 = 3 M1, which of the relationships below is correct?

L2=3L1
L1=3L2
L2=2L1-3L0
L2=3L1-2L0
L1=3(L2-L0)

when a force is applied to a spring, the force = k x where k is the spring constant and x is the distance displaced from equilibrium

the force acting on spring 1 is m1 g (the weight of m1), so we have

m1 g = k (L1 - L0) where L1 - L0 is the distance the spring is stretched from equilibrium

for m2, we have m2 g = k (L2-L0)

if m2 = 3m1, the second equation becomes

3 m 1 g= k(L2-L0) or m1 g = k(L2 - L0)/3

we also know that m 1 g = k (L1-L0), so equating these expressions

k(L1 - L0) = k(L2 - L0)/3 so that

3(L1 - L0) = L2 - L0

3 LI1 - 3 L0 = L2 - L0

L2 = 3 L1 - 2 L0

the fourth choice is correct