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.