Question

If the potential energy of conservative system is given by U(x) = (3x ^ 2 - 6x) (where x is in meter) then the equilibrium position is at x =​

Answer 1

Answer:

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Explanation:

where dU/dx=o i. e 6x-6=0=> when x= 1

Answer 2

Given: Potential energy of conservative system is given by U(x) = (3x ^ 2 - 6x)

To find: Equilibrium position is at x=?

Explanation: Equilibrium position is the point where the object is in complete balance, i.e, the force acting on it is zero.

Here, potential energy is denoted by:

$u(x) = 3 {x}^{2} - 6x$

Now the relation between force and potential energy is:

=>- du/dx= Force

=>$force = - \frac{d(3 {x }^{2} - 6x)}{dx}$

Formula for differentiation is:

$d( {a}^{n} ) = n {a}^{n - 1}$

Using this formula:

=>$force = - (6x - 6)$

But force=0 for equilibrium position

-(6x-6) =0

=> 6x= 6

=> x = 6/6

= 1 m

Therefore, the equilibrium position is option (b) at x= 1 m.