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Potential energy of a particle of mass 80 gm varies with its distance (x) from a fixed point on its line of motion according to the graph shown in the figure. Then time period of oscillation of the particle is

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$25 / π Hz$

$100 / π Hz$

$50 / π Hz$

$500 / π Hz$

answer is B.

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Detailed Solution

Energy of oscillation $= (0 .20 - 0 .04) J = 0 .16 J$

$∴ \frac{1}{2} \times \frac{80}{1000} \times {(\frac{4}{100})}^{2} . ω^{2} = 0 .16$

$\Rightarrow ω^{2} = 625 \times \frac{1}{4} \times 16 \Rightarrow ω = 50 rad / s$

$∴ f = \frac{ω}{2 π} = \frac{50}{2 π} Hz = 25 / π Hz$

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