A10-cm-long spring is attached to the ceiling. when a 2.0 kg mass is hung from it, the spring stretches to a length of 15 cm. how long when a 3.0 kg mass is suspended from it?

7.5 cm

Explanation:

The force exerted by the 2.0 kg on the spring is equal to the weight of the mass, so:

And this force causes a stretching of:

So we can use Hooke's law:

to find k, the spring constant:

Now a new mass of m = 3.0 kg is attached to the spring; the force applied by this mass is

So we can use again Hooke's law to find the new stretching: