What is the magnitude of the force required to stretch a 20 cm-long spring, with a spring constant of 100 n/m, to a length of 21 cm?

The correct answer to the question is: 1 N.

EXPLANATION:

As per the question, the spring constant or the force constant of the spring is given as k = 100 N/m.

The original length of the spring L = 20 cm.

The stretched length of the spring L'= 21 cm.

Hence, the change in length will be-

                              ∆L = L' - L

                                    = 21 cm - 20 cm

                                    = 1 cm

                                    = 0.01 m

We are asked to calculate the magnitude of force acting on the spring .

From Hooke's  law, we know that the restoring force that acts on the spring is proportional to the distance .

Mathematically it can be written as -

                F = - kx.

Here, k is the force constant.

         x is the change in length due to compression or elongation.

The negative sign is due to the fact that it is opposite to the applied force.

Hence, the applied force on the spring is calculated as -

            F = kx

               = k × ∆L

               = 100 N/ m × 0.01 m

               = 1 N.

Hence, the force acting on the spring is 1 N.

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