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When elongation in a rubber band is 3 cm, the stored energy in it is of magnitude E units. What will be the energy stored when the elongation is 6cm?


1.  E
2. 6E
3. 4E
4. 9E

1 Answer

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Best answer
Correct Answer - Option 3 : 4E

The correct answer is option 3) i.e. 4E.

CONCEPT:

Elastic potential energy: 

  • When we exert tensile stress on a wire, it will get stretched and work done in stretching the wire will be equal and opposite to the work done by inter-atomic restoring force.
  • This work stored in the wire in the form of Elastic potential energy.
  • It is given by the formula:

\(\Rightarrow U =\frac{1}{2}\times k\times (\delta X)^2\)

Where, U = Elastic potential energy, K = constant, δX = change in length

  • The elastic potential energy is directly proportional to the square of the change in length.

CALCULATION:

The energy of the rubber band when elongation is 3 cm = E

Let, the energy of the rubber band when elongation is 6 cm be E2.

Hence,

⇒ E2/E = (X2/X1)2

⇒ E2/E = (6/3)2

⇒ E2/E  = 4

⇒ E2 = 4E

  • Hence, energy stored at 6cm elongation will be 4E.

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