A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to- 

(1) x²

(2) e^x

(3) x

(4) log_e x

The spring extends by x on loading, then energy stored by the spring is : (if T is the tension in spring and k is spring constant) 

(1) $\frac{T^2}{2k}$

(2) $\frac{T^2}{2k^2}$

(3) $\frac{2k}{T^2}$

(4) $\frac{2T^2}{k}$

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. \(x=\sqrt[6]{\frac{2a}{b}}\)

Which one of the following is not a conservative force 

(1) Gravitational force

(2) Electrostatic force between two charges

(3) Magnetic force between two magnetic dipoles

(4) Frictional force

Work done in raising a box depends on

(1) How fast it is raised

(2) The strength of the man

(3) The height by which it is raised

(4) None of the above

If the kinetic energy of a body becomes four times of its initial value, then new momentum will

(1) Becomes twice its initial value

(2) Become three times its initial value

(3) Become four times its initial value

(4) Remains constant

If the water falls from a dam into a turbine wheel 19.6 m below, then the velocity of water at the turbine is (g = 9.8 m/s²) 

(1) 9.8 m/s

(2) 19.6 m/s

(3) 39.2 m/s

(4) 98.0 m/s

Two identical cylindrical vessels with their bases at the same level each contain a liquid of density; $\rho$. The height of the liquid in one vessel is h₁ and that in the other vessel is h₂ $\left(h_1>h_2\right)$.The area of either base is A. The work done by gravity in equalizing the levels when the two vessels are connected is :

(1) $(h_1-h_2)g\rho$

(2) $(h_1-h_2)gA\rho$

(3) $\frac{1}{2}{(h_1-h_2)}^{2}gA\rho$

(4) $\frac{1}{4}{(h_1-h_2)}^{2}gA\rho$

If the increase in the kinetic energy of a body is 21%, then the increase in the momentum will be:
1. 22%
2. 44%
3. 10%
4. 300%