Work, Energy and Power

A body of mass 2m moving with velocity v makes a head on elastic collision with another body of mass m which is initially at rest. Loss of kinetic energy of the colliding body (mass 2m) is

• 1/9  of its initial kinetic energy

• 1/6  of its initial kinetic energy 

• 8/9 of its initial kinetic energy

• 1/2 of its initial kinetic energy

Displacement x (in meters), of body of mass 1 kg as a function of time t, on a horizontal smooth surface is given as x = 2t² . The work done in the first one second by the external force is

• 1 J

• 2 J

• 4 J

• 8 J

Under the action of a constant force, a particle is experiencing a constant acceleration. The power is

• zero

• positive constant

• negative constant

• increasing uniformly with time

CO⁻ ion moving with kinetic energy of 20 keV dissociates into O⁻ and C which move along the parent ion direction. Assuming no energy is released during dissociation, the kinetic energy of the daughters (K.E)_O and (K.E)_C are related as

• (K.E)_O⁻ = (K.E)_C

• (K.E)_O⁻ / (K.E)_C = 16/12

• (K.E)_O⁻ / (K.E)_C = 12/16

• (K.E)_O⁻ / (K.E)_C = 16/28

The work-energy theorem states that the change in

• kinetic energy of a particle is equal to the work done on it by the net force

• kinetic energy of a particle is equal to the work done by one of the forces acting on it.

• potential energy of a particle is equal to the work done on it by the net force

• potential energy of a particle is equal to the work done by one of the forces acting on it

A car of masses 1500 kg is lifted up a distance of 30 m by crane A in 0.5 minutes. The second crane B does the same job in 1 minute. The ratio of their powers is

• 1 : 2

• 2 : 1

• 1 : 1

• 1 : 4

If the average kinetic energy of a molecule of a hydrogen gas at 300 K is E, then the average kinetic energy of a molecule of a nitrogen gas at the same temperature is

• 7 E

• E/14

• E

• E/7

A cricket ball is hit at an angle of 30° to the horizontal with a kinetic energy E. Its kinetic energy when it reaches the highest point is

• $\frac{\mathrm{E}}{2}$

• 0

• $\frac{2\mathrm{E}}{3}$

• $\frac{3\mathrm{E}}{4}$

A spring with force constant k is initially stretched by x₁. If it is further stretched by x₂, then the increase in its potential energy is

• $\frac{1}{2}\mathrm{k} ({\mathrm{x}}_2 - {\mathrm{x}}_1{)}^2$

• $\frac{1}{2} \mathrm{k} {\mathrm{x}}_2 ({\mathrm{x}}_2 + 2 {\mathrm{x}}_1)$

• $\frac{1}{2} \mathrm{k} {{\mathrm{x}}_1}^2 + \frac{1}{2} \mathrm{k} {{\mathrm{x}}_2}^2$

• $\frac{1}{2} \mathrm{k} ({\mathrm{x}}_1 + {\mathrm{x}}_2{)}^2$

A force F_x acts on a particle such that its position x changes as shown in the figure.

The work done by the particle as it moves from x = 0 to 20 m is

• 37.5 J

• 10 J

• 45 J

• 22.5 J