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The position of a particle (x) varies with time (t) as \(x = (t - 2)^2\), where x is in meters and t is in seconds. Calculate the work done during t = 0 to t = 4 s if the mass of the particle is 100 g.

1. 0.4 J

2. 0.2 J

3. 0.8 J

4. Zero

Subtopic: Work done by constant force |

61%

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A particle of mass m is moving in a circular path with a speed v = kt, where k is constant and t is time. The instantaneous power delivered to the particle is:

1. | Zero | 2. | mkt |

3. | ${\mathrm{mk}}^{2}\mathrm{t}$ | 4. | ${\mathrm{mk}}^{2}{\mathrm{t}}^{2}$ |

Subtopic: Power |

66%

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A position-dependent force $\mathrm{F}$ $=$ $6$ $+$ $8\mathrm{x}$ $-$ $3{\mathrm{x}}^{2}$ $\mathrm{N}$ acts on a small body of mass 3 kg, displacing it from x = 0 to x = 2 m. The work done in joule is:

1. 20 J

2. 40 J

3. 10 J

4. 12 J

Subtopic: Work Done by Variable Force |

82%

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A car of mass 100 kg and traveling at 20 m/s collides with a truck weighing 1 tonne traveling at 9 km/h in the same direction. The car bounces back at a speed of 5 m/s. The speed of the truck after the impact will be:

1. 11.5 m/s

2. 5 m/s

3. 18 m/s

4. 12 m/s

Subtopic: Collisions |

69%

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Which of the following remains unchanged (for the system) during an inelastic collision?

1. | Mechanical energy | 2. | Kinetic energy |

3. | Momentum | 4. | All of the above. |

Subtopic: Collisions |

76%

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An object of mass m = 1.5 kg is acted upon by the force as shown in the figure that varies with the position of the object as shown. If the object starts from rest at a point x = 0, then what is its speed at x = 50 m?

1. 20 m/s

2. 25 m/s

3. 15 m/s

4. 17 m/s

Subtopic: Work Energy Theorem |

80%

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The work done by a person in carrying a box of mass 10 kg to a vertical height of 10 m is 4900 J. The mass of the person is:

1. 40 kg

2. 60 kg

3. 50 kg

4. 55 kg

Subtopic: Gravitational Potential Energy |

69%

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The principle of conservation of energy implies that:

1. the total mechanical energy is conserved.

2. the total kinetic energy is conserved.

3. the total potential energy is conserved.

4. the sum of all types of energies is conserved.

Subtopic: Conservation of Mechanical Energy |

54%

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The potential energy \(\mathrm{U}\) of a system is given by $\mathrm{U}=$ $\mathrm{A}$ $-$ ${\mathrm{Bx}}^{2}$ (where \(\mathrm{x}\) is the position of its particle and \(\mathrm{A},\) \(\mathrm{B}\) are constants). The magnitude of the force acting on the particle is:

1. constant

2. proportional to \(\mathrm{x}\)

3. proportional to ${\mathrm{x}}^{2}$

4. proportional to $\left(\frac{1}{\mathrm{x}}\right)$

Subtopic: Potential Energy: Relation with Force |

84%

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A person-1 stands on an elevator moving with an initial velocity of 'v' & upward acceleration 'a'. Another person-2 of the same mass m as person-1 is standing on the same elevator. The work done by the lift on the person-1 as observed by person-2 in time 't' is:

1. $\mathrm{m}\left(\mathrm{g}\right)$ $+$ $\mathrm{a}\left(\mathrm{vt}\right)$ $+$ $\frac{1}{2}{\mathrm{at}}^{2}$

2. $-\mathrm{mg}\left(\mathrm{vt}\right)$ $+$ $\frac{1}{2}{\mathrm{at}}^{2}$

3. 0

4. $\mathrm{ma}\left(\mathrm{vt}\right)$ $+$ $\frac{1}{2}{\mathrm{at}}^{2}$

Subtopic: Work done by constant force |

79%

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