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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 |

67%

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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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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 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 $(5\hat{\mathrm{i}}-3\hat{\mathrm{j}}+6\hat{\mathrm{k}})$m/s under the influence of a constant force $\overrightarrow{F}=(10\hat{\mathrm{i}}+10\hat{\mathrm{j}}+20\hat{\mathrm{k}})$ N. The instantaneous power applied to the particle is:

1. | 200 J/s | 2. | 40 J/s |

3. | 140 J/s | 4. | 170 J/s |

Subtopic: Power |

91%

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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 = 4s is:

1. | 8 J | 2. | 4 J |

3. | 0 J | 4. | Can't be determined |

Subtopic: Work done by constant force |

57%

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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 |

60%

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The potential energy of a particle varies with distance r as shown in the graph. The force acting on the particle is equal to zero at:

1. | P | 2. | S |

3. | Both Q and R | 4. | Both P and S |

Subtopic: Potential Energy: Relation with Force |

87%

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A block of mass m is placed in an elevator moving down with an acceleration $\frac{\mathrm{g}}{3}$. The work done by the normal reaction on the block as the elevator moves down through a height h is:

1. $\frac{-2\mathrm{mgh}}{3}$

2. $\frac{-\mathrm{mgh}}{3}$

3. $\frac{2\mathrm{mgh}}{3}$

4. $\frac{\mathrm{mgh}}{3}$

Subtopic: Work done by constant force |

65%

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A particle is moving such that the potential energy U varies with position in metre as U (x) = ($4{\mathrm{x}}^{2}$ - 2x + 50) J. The particle will be in equilibrium at:

1. x = 25 cm

2. x = 2.5 cm

3. x = 25 m

4. x = 2.5 m

Subtopic: Potential Energy: Relation with Force |

78%

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