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Q.

Potential energy of a particle executing SHM is U at an instant. Magnitude of  acceleration is a at the same instant. If x is the magnitude of displacement of the  particle

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a

U is proportional to x

b

a is proportional to x

c

U is proportional to  x2

d

Both (2) and (3)

answer is D.

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Detailed Solution

For simple harmonic motion, the potential energy can be written as  U=12Kx2  ⇒U  α  x2---(1) . Differentiating with respect to x we get  dUdx=−Kx.  here K =force constant ; x = displacement; m=mass of the oscillatorHere dUdx  is the force due to simple harmonic motion which can be equated to  ma.    force F= ma=−Kx.   acceleration =a=−Kxm                                    ⇒a  α  x---(2)equations (1) and (2) are the reasons for the options chosen
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