Question

A body of mass 8 kg is suspended through two light springs X and Y connected in series as shown in figure. The readings in X and Y respectively are:

A.)Zero, 8 kg
B.)2 kg, 6 kg
C.)6 kg, 2 kg
D.)8 kg, 8 kg

Answer 1

Hint: Define how forces on spring works. Obtain the mathematical expression for spring constant. Find out the force on each spring with the concept of restoring force of spring or the tension in the spring.

Complete step by step answer:
The two springs are connected to each other and at the end of one we have a 8 kg mass suspended. Now, because of the suspension of the mass on the spring there will be a weight on the springs. Due to this weight the springs will elongate.

Let the spring X will elongate by a distance x and the spring y will elongate by a distance y.
Let the weight or the downward force on the spring Y will be 8g, where g is the acceleration due to gravity. So, the spring Y will elongate by a distance y and the restoring force or tension on the spring Y will be ${{k}_{1}}y$, where ${{k}_{1}}$ is the spring constant of the spring Y.
${{k}_{1}}y=8g$

Now, the spring X will also feel the downward force ${{k}_{1}}y$ due to which the spring will elongate by a length x. so the restoring force or the tension on the spring X will be ${{k}_{2}}x$, where ${{k}_{2}}$ is the spring constant of the spring X.
${{k}_{2}}x={{k}_{1}}y$

From the above two equation we can write that,

${{k}_{2}}x={{k}_{1}}y=8g$

So, both the spring will feel the same downward force i.e. they will give the same readings.
So, the spring X will read 8 kg and spring Y will also read 8 kg.
The correct option is (D).

Note: When a spring is stretched or compressed by an external force its length changes from the equilibrium. The force exerts by the spring to go to the equilibrium position again is called the restoring force of the spring. The restoring force is directly proportional to the displacement from the equilibrium position of the spring.