Potential energy (U) related to coordinates is given by U = 3(x + y). Work done by the conservative force when the particle is going from (0, 0), (2, 3) is:
1. 15 J
2. -15 J
3. 12 J
4. 10 J
The potential energy of a body is given by, U = A – Bx2 (Where x is the displacement). The magnitude of force acting on the particle is
(1) Constant
(2) Proportional to x
(3) Proportional to x2
(4) Inversely proportional to x
The potential energy between two atoms in a molecule is given by \(U\left ( x \right )=\frac{a}{x^{12}}-\frac{b}{x^{6}};\) where \(a\) and \(b\) are positive constants and \(x\) is the distance between the atoms. The atoms are in stable equilibrium when:
1. \(x=\sqrt[6]{\frac{11a}{5b}}\)
2. \(x=\sqrt[6]{\frac{a}{2b}}\)
3. \(x=0\)
4. \(x=\sqrt[6]{\frac{2a}{b}}\)
A particle free to move along the x-axis has potential energy given by for , where k is a positive constant of appropriate dimensions. Then
(1) At point away from the origin, the particle is in unstable equilibrium
(2) For any finite non-zero value of x, there is a force directed away from the origin
(3) If its total mechanical energy is k/2, it has its minimum kinetic energy at the origin
(4) For small displacements from x = 0, the motion is simple harmonic
A particle which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as . Here k and a are positive constants. For , the functional form of the potential energy U(x) of the particle is-
(1)
(2)
(3)
(4)
The potential energy of a system is represented in the first figure. the force acting on the system will be represented by:
1. | 2. | ||
3. | 4. |
The force acting on a body moving along x-axis varies with the position of the particle as shown in the fig.
The body is in stable equilibrium at
(1) x = x1
(2) x = x2
(3) both x1 and x2
(4) neither x1 nor x2
The potential energy of a particle varies with distance x as shown in the graph. The force acting on the particle is zero at
(1) C
(2) B
(3) B and C
(4) A and D
The diagrams represent the potential energy U as a function of the inter-atomic distance r. Which diagram corresponds to stable molecules found in nature.
(1)
(2)
(3)
(4)
The potential energy of a system increases if work is done
(1) by the system against a conservative force
(2) by the system against a nonconservative force
(3) upon the system by a conservative force
(4) upon the system by a nonconservative force