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

A bomb of 12 kg explodes into two pieces of masses 4 kg and 8 kg. The velocity of 8kg mass is 6 m/sec. The kinetic energy of the other mass is 

(1) 48 J

(2) 32 J

(3) 24 J

(4) 288 J

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

A bullet is fired from a rifle. If the rifle recoils freely, then the kinetic energy of the rifle is 

(1) Less than that of the bullet

(2) More than that of the bullet

(3) Same as that of the bullet

(4) Equal or less than that of the bullet

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%

If a body of mass 200 g falls from a height 200 m and its total P.E. is converted into K.E. at the point of contact of the body with earth surface, then what is the decrease in P.E. of the body at the contact (g = 10 m/s²) 

(1) 200 J

(2) 400 J

(3) 600 J

(4) 900 J