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Work Energy and Power question

2003 · Q157
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Work Energy and Power question

2003 · Q157

NEETPhysicsWork Energy and PowerMCQ+4 / −1
When a long spring is stretched by 2 cm, its potential energy is U. If the spring is stretched by 10 cm, the potential energy stored in it will be
  1. A
    U/5
  2. B
    5U
  3. C
    10U
  4. D
    25U
View written solutionFree

Correct answer: D

If k be the spring constant, then

U=12×k×(2)2=2kU = {1 \over 2} \times k \times {\left( 2 \right)^2} = 2kU=21​×k×(2)2=2k

Ufinal=12×k×(10)2=50k{U_{final}} = {1 \over 2} \times k \times {\left( {10} \right)^2} = 50kUfinal​=21​×k×(10)2=50k

⇒UUfinal=2k50k=125 \Rightarrow {U \over {{U_{final}}}} = {{2k} \over {50k}} = {1 \over {25}}⇒Ufinal​U​=50k2k​=251​

⇒Ufinal=25U \Rightarrow {U_{final}} = 25U⇒Ufinal​=25U

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