Five balls are placed one after another along a straight line as shown in the figure. Initially, all the balls are at rest. Then the second ball is projected with speed ${\mathrm{v}}_0$ towards the third ball. Mark the correct statement(s). (Assume all collisions to be head-on and elastic):
     

1. The total number of collisions in the process is 5.

2. The velocity of separation between the first and fifth ball after the last possible collision is ${\mathrm{v}}_{0.}$

3. Finally, three balls remain stationary.

4. All of the above are correct.

A body of mass \(2\) kg moving with a velocity of \(3\) m/s collides with a body of mass of \(1\) kg moving with a velocity of \(4\) m/s in the opposite direction. If the collision is head-on and completely inelastic, then the wrong statement is:

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 \({z}\)-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 \({x}\)-axis, \({y}\)-axis and \({z}\)-axis of the system respectively. The work done by this force in moving the body a distance of \(4~\text m\) along the \({z}\)-axis will be:
1. \(15~\text J\) 
2. \(14~\text J\) 
3. \(13~\text J\) 
4. \(12~\text J\) 

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

Which one of the following statement is wrong?