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The potential energt of a particle of ma...

The potential energt of a particle of mass 0.1 kg, moving along the x-axis, is given by `U=5x(x-4)J`, where x is in meter. It can be concluded that

A

The particle excute `SHM` with mea n position at `x = 4 m`

B

The particle excute `SHM` with mea n position at `x = 2 m`

C

The particle excute `SHM` with time period `pi//5` second

D

The particle excutre `SHM` with time period `pi//10` second

Text Solution

Verified by Experts

The correct Answer is:
B,C

`U = 5x^(2) - 20x rArr F = - (dU)/(dx) = - 10 x + 20 = - 10(x-2)`
Acceleration `a = (F)/(m) = - 100(x-2)` so `omega^(2) = 100 rArr omega = 10`
Time period `T = (2pi)/(omega) = (2pi)/(10) = (pi)/(5)` sec
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