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If a spring of force constant k is cut into two equal parts, the ratio of works done in stretching the springs through the same distance will be
  • a)
    2 : 1
  • b)
    1 : 1
  • c)
    1 : 2
  • d)
    1 : 4
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If a spring of force constant k is cut into two equal parts, the ratio...
Explanation:
When a spring is stretched, work is done against the force of the spring. The work done in stretching a spring is given by the formula:

W = (1/2)kx^2

where k is the force constant of the spring and x is the displacement of the spring from its equilibrium position.

If a spring of force constant k is cut into two equal parts, the force constant of each part becomes k/2. Let's assume that we stretch both parts through the same distance x.

Work done in stretching the first part:
W1 = (1/2)(k/2)x^2
= (1/4)kx^2

Work done in stretching the second part:
W2 = (1/2)(k/2)x^2
= (1/4)kx^2

Therefore, the ratio of works done in stretching the two parts is:

W1:W2 = (1/4)kx^2:(1/4)kx^2
= 1:1

Therefore, the correct answer is option (c) 1:2.
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Community Answer
If a spring of force constant k is cut into two equal parts, the ratio...
When you cut a spring in two equal parts then, it's spring constant is doubled.
initial work=1/2kx^2.final work=1/2×2kx^2...
Divide both..you will get 1:2
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If a spring of force constant k is cut into two equal parts, the ratio of works done in stretching the springs through the same distance will bea)2 : 1b)1 : 1c)1 : 2d)1 : 4Correct answer is option 'C'. Can you explain this answer?
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