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:

1. Both bodies move together with a velocity (2/3) m/s.

2. The momentum of the system is 2 kg-m/s throughout.

3. The momentum of the system is 10 kg-m/s.

4. The loss of KE for the system is (49/3) J.

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 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 \(V(x)=\frac{kx^2}{2}\), 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. \(\mathrm{x}=\pm 1\) m
2. \(\mathrm{x}=\pm 2\) m
3. \(\mathrm{x}=\pm 3\) m
4. \(\mathrm{x}=\pm 4\) m$\mathrm{}$

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