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Work Energy and Power question

2006 · Q159
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Work Energy and Power question

2006 · Q159

NEETPhysicsWork Energy and PowerMCQ+4 / −1
The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm the potential energy stored in it is
  1. A
    U/4
  2. B
    4U
  3. C
    8U
  4. D
    16U
View written solutionFree

Correct answer: D

Potential energy of a spring

= 12{1 \over 2}21​ ×\times× force constant ×\times× (extension)2

∴\therefore∴ Potential energy ∝\propto∝ (extension)2

or, U1U2=(x1x2)2{{{U_1}} \over {{U_2}}} = {\left( {{{{x_1}} \over {{x_2}}}} \right)^2}U2​U1​​=(x2​x1​​)2 or, U1U2=(28)2{{{U_1}} \over {{U_2}}} = {\left( {{2 \over 8}} \right)^2}U2​U1​​=(82​)2

⇒U1U2=116 \Rightarrow {{{U_1}} \over {{U_2}}} = {1 \over {16}}⇒U2​U1​​=161​

⇒U2=16U1=16U  (∵U1=U) \Rightarrow {U_2} = 16{U_1} = 16U\,\,\left( {\because{U_1} = U} \right)⇒U2​=16U1​=16U(∵U1​=U)

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