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

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