A particle of mass $10 g$ lies in a potential field $v = 50 x^{2} + 100$ . The value of frequency of oscillations in Hz is:

5 H z

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50 / π H z

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10 π / 3 H z

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none of these.

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Solution

The correct option is B $50 / π H z$
$v = 50 x^{2} + 100 F = - \frac{d v}{d x} F = - 100 x a = - \frac{100 x}{10} \times 1000 a = - 10^{4} x$
Comparing with $a = ω^{2} x$
$ω = \sqrt{10^{4}} = 10^{2} T = \frac{2 π}{ω} T = \frac{π}{50} v = \frac{1}{T} = \frac{50}{π} H z$

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A particle of mass 10 gm lies in a potential field $V = 50 x^{2} + 100$ . The value of frequency of oscillations in Hz is

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\frac{25}{π} H z

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