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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