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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

Subtopic: Concept of Work |

89%

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The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?

1. 2.5 m/s

2. 3.9 m/s

3. 4.7 m/s

4. 5.3 m/s

Subtopic: Work Energy Theorem |

57%

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A body of mass 0.5 kg travels in a straight line with velocity $\mathrm{v}={\mathrm{ax}}^{3/2}$where $\mathrm{a}=5{\mathrm{m}}^{-1/2}{\mathrm{s}}^{-1}$. What is the work done by the net force during its displacement from x = 0 to x = 2 m?

1. 50 J

2. 45 J

3. 68 J

4. 90 J

Subtopic: Work Energy Theorem |

63%

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A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down at a uniform speed of 7 m/s. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact?

1. 8.82 J

2. 7.65 J

3. 7.01 J

4. 7.98 J

Subtopic: Gravitational Potential Energy |

59%

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A body of mass 'm' is released from the top of a fixed rough inclined plane as shown in the figure. If the frictional force has magnitude F, then the body will reach the bottom with a velocity: $(\mathrm{L}=\sqrt{2}\mathrm{h})$

1. | \(\sqrt{2 g h} \) | 2. | \(\sqrt{\frac{2 F h}{m}} \) |

3. | \(\sqrt{2 g h+\frac{2 F h}{m}} \) | 4. | \(\sqrt{2 g h-\frac{2 \sqrt{2} F h}{m}}\) |

Subtopic: Work Energy Theorem |

62%

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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 |

66%

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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. $\frac{Fh}{2}$

4. 4Fh

Subtopic: Work done by constant force |

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The potential energy of a system increases if work is done:

1. by the system against a conservative force.

2. by the system against a non-conservative force.

3. upon the system by a conservative force.

4. upon the system by a non-conservative force.

Subtopic: Potential Energy: Relation with Force |

58%

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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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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 |

66%

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