The question states that a spring with length T and spring constant k is cut into two pieces of lengths lv and Z2, such that lv = nl.

To find the force constant of the spring with length lv, we can use Hooke`s Law, which states that the force exerted by a spring is directly proportional to its displacement from equilibrium. Mathematically, this can be represented as F = -kx, where F is the force, k is the spring constant, and x is the displacement.

In this case, the displacement of the spring of length lv can be represented as x = nl. Therefore, the force constant, denoted as k`, can be calculated by rearranging Hooke`s Law:

F = -k` * (nl)

Since both springs are cut from the same original spring, they should have the same spring constant. Therefore, we can equate the force constant of the original spring (k) to the force constant of the spring of length lv (k`):

k = -k` * (nl)

Rearranging this equation, we can solve for k`:

k` = -k / (nl)

Simplifying further, we get:

k` = -k / (n * l)

Multiplying