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A body of mass m is in a field where its...

A body of mass `m` is in a field where its potential energy is given by `U = ax^(3) +bx^(4)`, where `a` and `b` are positive constants. Then, [The body moves only along `x`]

A

`x = 0` is a point of equilibrium

B

`x = (-3a)/(4b)` is a point of stable equilibrium

C

`x = (-3a)/(4b)` is a point of unstable equilibrium

D

for small displacements from stable equilibrium position the body executes `SHM` with angular frequency `(3a)/(2sqrt(bm))`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`U = ax^(3) +bx^(4)`
`F = (delU)/(delx)= -3ax^(2) - 4bx^(3)`
`F = 0 at x = 0` and `x = (-3a)/(4b)`
For small displacement restoring force is given by,
`F_(res) = (9a^(2))/(4b) deltax`
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Knowledge Check

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