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The potential energy of a particle movin...

The potential energy of a particle moving along x-axis is given by `U = 20 + 5 sin (4 pi x)`, where `U` is in `J` and `x` is in metre under the action of conservative force :

A

if total mechanical energy is `20 J`,
then at `x = 7//8 m`, particle is at equilibrium

B

if total mechanical energy is `20 J`,
then at `x = 7//8 m` particle is not at equilibrium

C

if total mechanical energy is `20 J`,
then at `x = 3//8 m`, particle is at equilibrium

D

if total mechanical energy is `20 J`,
then at `x = 3//8 m`, particle is not at equilibrium.

Text Solution

Verified by Experts

The correct Answer is:
A, C
`U_(min)` is at `sin(4 pix) = -1`
`U_(min) = 20 -5 = 15 J`
`K_(max) =E-U_(min) = 20 - 15 = 5 J`
`4 pi x=(3)/(2)pi,(7)/(2)p , x = (3)/(8),(7)/(8),....`.
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