Question

8.
In a certain field, the potential energy is U = ax? -
bx, where a and b constants. The particle is in stable
equilibrium at x equal to
(1) Zero
BY 36
(3) za​

Answer 1

Answer: correct option is (1)

Explanation: because when we plot the graph . the graph will be of opening downwards and in these type of graphs the point is only of maxima ...so as we know that at stable equilibrium there should be point of minima so answer will be at x= 0

Answer 2

Answer:

The particle is in stable  equilibrium at $x=\dfrac{b}{2a}$.

Explanation:

Given that,

The potential energy is

$U=ax^2-bx$

On differentiating

$\dfrac{dU}{dt}=2ax-b$...(I)

We need to calculate the particle is in stable

For $\dfrac{dU}{dt}=0$

From equation (I)

$2ax-b=0$

$x=\dfrac{b}{2a}$

Hence, The particle is in stable  equilibrium at $x=\dfrac{b}{2a}$.