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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. |

Subtopic: Collisions |

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The power supplied to a particle of mass 2 kg varies with time as $\mathrm{P}=\frac{3{\mathrm{t}}^{2}}{2}$ Watt, where t is in seconds. If the velocity of a particle at t = 0 is v = 0, then the velocity of the particle at t = 2 s will be:

1. | \(1 \mathrm{~m} / \mathrm{s} \) | 2. | \(4 \mathrm{~m} / \mathrm{s} \) |

3. | \(2 \mathrm{~m} / \mathrm{s} \) | 4. | \(2 \sqrt{2} \mathrm{~m} / \mathrm{s}\) |

Subtopic: Power |

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The potential energy of a 1 kg particle free to move along the x-axis is given by:

$\mathrm{U}\left(\mathrm{x}\right)=\left(\frac{{\mathrm{x}}^{4}}{4}-\frac{{\mathrm{x}}^{2}}{2}\right)\mathrm{J}$

The total mechanical energy of the particle is 2J. Then, the maximum speed (in ms^{-1}) will be

1. \(3 \over \sqrt{2} \)

2. \(\sqrt{2}\)

3. \(1 \over \sqrt{2}\)

4. 2

Subtopic: Conservation of Mechanical Energy |

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A particle moves with a velocity of \(\left(5\hat{i}-3\hat{j}+6\hat{k}\right)\text{m/s}\) under the influence of a constant force \(\vec F = \left(10\hat{i}+10\hat j +20\hat k\right) \text{N} \). The instantaneous power applied to the particle is:

1. | \(200~\text{J/s}\) | 2. | \(40~\text{J/s}\) |

3. | \(140~\text{J/s}\) | 4. | \(170~\text{J/s}\) |

Subtopic: Power |

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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.

Subtopic: Collisions |

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The position-time graph of a particle of mass \(2\) kg is shown in the figure. Total work done on the particle from \(t=0\) to \(t=4\) s is:

1. \(8\) J

2. \(4\) J

3. \(0\) J

4. can't be determined

Subtopic: Work done by constant force |

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A water pump rated \(400~\text{W}\) has an efficiency of \(75\%\). If it is employed to raise water to a height of \(40~\text{m}\), then the volume of water drawn in \(10~\text{min}\) is:

1. \(10.9~\text{m}^{3}\)

2. \(0.45~\text{m}^{3}\)

3. \(1.8~\text{m}^{3}\)

4. \(0.25~\text{m}^{3}\)

1. \(10.9~\text{m}^{3}\)

2. \(0.45~\text{m}^{3}\)

3. \(1.8~\text{m}^{3}\)

4. \(0.25~\text{m}^{3}\)

Subtopic: Power |

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In the diagram shown, force \(F\) acts on the free end of the string. If the weight \(W\) moves up slowly by distance \(h,\) then work done on the weight by the string holding it will be: (pulley and string are ideal)

1. \(Fh\)

2. \(2Fh\)

3. \(Fh/2\)

4. \(4Fh\)

Subtopic: Work done by constant force |

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The diagram represents a particle's potential energy curve in a field. The particle will be in equilibrium at which position(s):

1. \(B\) and \(D\)

2. \(A\) and \(C\)

3. \(A,B\) and \(C\)

4. \(A,B,C\) and \(D\)

Subtopic: Potential Energy: Relation with Force |

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A particle of mass 'm' is projected at an angle '$\mathrm{\alpha \text{'}}$ with the horizontal, with an initial velocity 'u'. The work done by gravity during the time it reaches its highest point is:

1. ${u}^{2}{\mathrm{sin}}^{2}a$

2. $\frac{m{u}^{2}{\mathrm{cos}}^{2}\alpha}{2}$

3. $\frac{m{u}^{2}{\mathrm{sin}}^{2}\alpha}{2}$

4. $-\frac{m{u}^{2}{\mathrm{sin}}^{2}\alpha}{2}$

Subtopic: Gravitational Potential Energy |

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