A particle is moving on x-axis has potential energy $U = 2 - 20 x + 5 x^{2}$ J along x-axis. The particle is released at x=-3. The maximum value of x will be [x is in meter and U is in joule]

5 m

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3 m

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7 m

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8 m

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Solution

The correct option is C
7 m

$U = 2 - 20 x + 5 x^{2}; F = - \frac{d U}{d x} = - 20 + 10 x$

At equilibrium position, F = 0

$20 - 10 x = 0 \Rightarrow x = 2$

It will oscillate about x = 2 with amplitude of 5 m.

$∴$ maximum value of x will be 7 m.

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