The extension of a stretched string is directly proportional to its tension. If the extension produced by a tension of 8 Newtons is 2cm, find the extension ...

The extension of a stretched string is directly proportional to its tension. If the extension produced by a tension of 8 Newtons is 2cm, find the extension produced by a tension of 12 Newtons.

Answer Details

Since the extension of a stretched string is directly proportional to its tension, we can use the formula:

extension = k * tension

where k is a constant of proportionality. We can find k by using the known values of tension and extension:

k = extension / tension
k = 2 cm / 8 N = 0.25 cm/N

Now that we have found k, we can use it to find the extension produced by a tension of 12 Newtons:

extension = k * tension
extension = 0.25 cm/N * 12 N = 3 cm

So, the extension produced by a tension of 12 Newtons is 3 cm.