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A heavy stone is thrown from a cliff of height \(h\) with a speed \(v.\) The stone will hit the ground with maximum speed if it is thrown:

1. | vertically downward |

2. | vertically upward |

3. | horizontally |

4. | the speed does not depend on the initial direction |

Subtopic: Work Energy Theorem |

59%

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Two springs \(\mathrm{A}\) and \(\mathrm{B}\) \((k_A=2k_B)\) are stretched by applying forces of equal magnitudes at the four ends. If the energy stored in \(\mathrm{A}\) is \(E,\) that in \(\mathrm{B}\) is:

1. \(\frac{E}{2}\)

2. \(2E\)

3. \(E\)

4. \(\frac{E}{4}\)

Subtopic: Elastic Potential Energy |

57%

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Two equal masses are attached to the two ends of a spring of spring constant k. The masses are pulled out symmetrically to stretch the spring by a length x over its natural length. The work done by the spring on each mass is

1. \(\frac{1}{2} \mathrm{kx}^{2}\)

2. \(-\frac{1}{2} \mathrm{kx}^{2}\)

3. \(\frac{1}{4} \mathrm{kx}^{2}\)

4. \(-\frac{1}{4} \mathrm{kx}^{2}\)

Subtopic: Elastic Potential Energy |

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The negative of the work done by the conservative internal forces on a system equals the change in:

1. total energy

2. kinetic energy

3. potential energy

4. none of these

Subtopic: Elastic Potential Energy |

71%

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The work done by the external forces on a system equals the change in:

1. total energy

2. kinetic energy

3. potential energy

4. none of these

Subtopic: Concept of Work |

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The work done by all the forces (external and internal) on a system equals the change in:

1. | total energy | 2. | kinetic energy |

3. | potential energy | 4. | none of these |

Subtopic: Work Energy Theorem |

73%

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__________ of a two-particle system depends only on the separation between the two particles. The most appropriate choice for the blank space in the above sentence is:

1. kinetic energy

2. total mechanical energy

3. potential energy

4. total energy

Subtopic: Gravitational Potential Energy |

78%

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A small block of mass \(m\) is kept on a rough inclined surface of inclination \(\theta\) fixed in an elevator. The elevator goes up with a uniform velocity \(v\) and the block does not slide on the wedge. The work done by the force of friction on the block in time \(t\) will be:

1. zero

2. \(mgvt ~cos^2\theta\)

3. \(mgvt ~sin^2\theta\)

4. \(mgvt ~sin2\theta\)

Subtopic: Concept of Work |

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A block of mass \(m\) slides down a smooth vertical circular track. During the motion, the block is in:

1. vertical equilibrium

2. horizontal equilibrium

3. radial equilibrium

4. none of these

Subtopic: Concept of Work |

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A particle is rotated in a vertical circle by connecting it to a string of length I and keeping the other end of the string fixed. The minimum speed of the particle when the string is horizontal for which the particle will complete the circle is

1. \(\sqrt{\mathrm{g} l}\)

2. \(\sqrt{2 \mathrm{~g} l}\)

3. \(\sqrt{3 \mathrm{~g} l}\)

4. \(\sqrt{5 \mathrm{~g} l}\)

Subtopic: Work Energy Theorem |

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