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Question
If there are two springs A and B of stiffness KA and KB respectively, and if KA > KB, then on application of the same force, work done is more in
A.
B
B.
A
C.
Same in both
D.
Information insufficient
Answer ( Option A)

B

Solution

The work done by a spring is given by the equation:
     
Where W is the work done, k is the stiffness of the spring, and x is the displacement of the spring from its equilibrium position.
If we apply the same force to both springs A and B, the displacement x will be different for each spring because the stiffness KA is greater than KB. This means that for the same force, spring A will be stretched or compressed less than spring B.
Since the work done is directly proportional to the square of the displacement, the spring with a larger displacement will do more work. In this case, since spring B has a larger displacement than spring A, the work done will be more in spring B.
Hence, the correct option is (a)

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