Consider the potential energy given by `U(x)=-(x^(4))/(4)-(x^(3))/(3)+x^(2)` where the coefficients of the various powers of x have units such that U has units of joules. Find the equilibrium points and classify them.

Consider the algebraic expression 4x^(3)-y-2x^(2)+(3)/(2)xy^(2)-6x What is the coefficient of x2 in the term 4x^(3)y ?

The potential energy of a body is given by U = A - Bx^(2) (where x is the displacement). The magnitude of force acting on the partical is

Find the extrema points of f(x)=3x^(4)-4x^(3)-36x^(2)+28

Potential energy function along x- axis in a certain force field is given as U(x)=(x^(4))/(4)-2x^(2)+(11)/(2)x^(2)-6x For the given force field :- (i)the points of equilibrium are x=1 , x=2 and x=3 (ii) the point x=2 is a point of unstable equilibrium. (iii) the points x=1 and x=3 are points of stable equilibrium. (iv) there exists no point of neutral equilibrium. The correct option is :-

The potential energy for a conservative system is given by U=(x^(3))/(3)-(5x^(2))/(2)+6x+3. Match all the entries in Column l to all the entries in Column II.

The cost function of a product is given by C(x)=(x^(3))/(3)-45x^(2)-900x+36 where x is the number of units produced. How many units should be produced to minimise the marginal cost ?

Find the coefficient of x^4 in (1 - 4x)^(-3//5)

Let gravitational potential energy U is given by U=Asqrtx/(B+x^2) , where x is distance. The dimensional formula of A/B is

The potential energy between two atoms in a molecule is given by U(x)= (a)/(x^(12))-(b)/(x^(6)) , where a and b are positive constants and x is the distance between the atoms. The atom is in stable equilibrium when

The potential energy between two atoms in a molecule is given by U=ax^(2)-bx^(2) where a and b are positive constants and x is the distance between the atoms. The atom is in stable equilibrium when x is equal to :-