If a force of 10 N stretches a certain spring 4cm, How much stretch will occur for an applied force of 15 N?

For spring system

Force applied

F = - kx

Where k is the spring constant and x is stretching length of spring. The negative sign indicates that force applied to strech a spring produces a negative acceleration in spring which give rise to restoring force.

Now

In first step

F = 10N

x = 4 cm = 0.04 m

Since k is a constant thus

k = F/x = 10/0.04 = 250 N/m

Which will be the spring constant of the spring.

In second step 15 N force is applied to the same string.

Thus, the streching length can be calculated as

x = F / k = 15 N / 250 N/m = 0.06 m = 6 cm