Which one of the following statements is true?

1. In an elastic collision of two bodies, the momentum, and energy of each body is conserved.
2. Total energy of a system is always conserved, no matter what internal and external forces on the body are present.
3. Work done in the motion of a body over a closed loop is zero for every force in nature.
4. Usually in an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.

A body is initially at rest. It undergoes a one-dimensional motion with constant acceleration. The power delivered to it at time \(t\) is proportional to,
1. \( t^{1 / 2} \)
2. \(t \)
3. \(t^{3 / 2} \)
4. \(t^2\)$\mathrm{}$

A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time \(t\) is proportional to,
1. \(t^{1/2}\)
2. \(t\)
3. \(t^{3/2}\)
4. \(t^{2}\)

A body constrained to move along the \(\mathrm{z}\)-axis of a coordinate system is subjected to constant force given by \(\vec{F}=-\hat{i}+2 \hat{j}+3 \hat{k}\) where \(\hat{i},\hat{j} \) and \(\hat{k}\) are unit vectors along the \(\mathrm{x}\)-axis, \(\mathrm{y}\)-axis and \(\mathrm{z}\)-axis of the system respectively. The work done by this force in moving the body a distance of \(4\) m along the \(\mathrm{z}\)-axis will be:
1. \(15\) J
2. \(14\) J
3. \(13\) J
4. \(12\) J

A pump on the ground floor of a building can pump up water to fill a tank of volume$30 m^3$ in 15 min. If the tank is 40 m above the ground and the efficiency of the pump is 30%. Then electric power consumed by the pump is:
1. 44.4 kW
2. 44 kW
3. 40.7 kW
4. 45 kW

A body of mass 2 kg initially at rest moves under the action of an applied horizontal force of 7 N on a table with a coefficient of kinetic friction = 0.1. The work done by the applied force in 10 s is:

1. 882 J
2. 635 J
3. 247 J
4. 120 J

The potential energy function for a particle executing linear simple harmonic motion is given by \(V(x)=\dfrac{kx^2}{2}\), where \(k\) is the force constant of the oscillator. For \(k=0.5\) N/m, the graph of \(V(x)\) versus \(x\) is shown in the figure. A particle of total energy \(1\) J moving under this potential must turn back when it reaches:

      
1. \({x}=\pm 1\) m
2. \({x}=\pm 2\) m
3. \({x}=\pm 3\) m
4. \({x}=\pm 4\) m

Which one of the following statement is wrong?

An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy 10 keV, and the second with 100 keV. The ratio of their speeds is:

($m_e$ = $9.31\times {10}^{-31} kg$, $m_p$ = $1.67\times {10}^{-27} kg$, 1 eV = $1.60\times {10}^{-19} kg$).

1. 13.5: 1
2. 1: 1
3. 1: 13.5
4. 2: 1

A raindrop of radius \(2\) mm falls from a height of \(500\) m above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until, at half its original height, it attains its maximum (terminal) speed, and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey?