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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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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 |

66%

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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 |

88%

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The potential energy of a particle of mass 1 kg free to move along the X-axis is given by \(U(x) = (3x^2-4x+6)~\text{J}\). The force acting on the particle at x = 0 will be:

1. 2$\hat{\mathrm{i}}$ N

2. -4$\hat{\mathrm{i}}$ N

3. 5$\hat{\mathrm{i}}$ N

4. 4$\hat{\mathrm{i}}$ N

Subtopic: Potential Energy: Relation with Force |

61%

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A block of mass 'm' is connected to a spring of force constant K. Initially, the block is at rest and the spring is relaxed. A constant force F is applied horizontally towards the right. The maximum speed of the block will be:

1. | $\frac{\mathrm{F}}{\sqrt{2\mathrm{mK}}}$ | 2. | $\frac{\sqrt{2}\mathrm{F}}{\sqrt{\mathrm{mK}}}$ |

3. | $\frac{\mathrm{F}}{\sqrt{\mathrm{mK}}}$ | 4. | $\frac{2\mathrm{F}}{\sqrt{2\mathrm{mK}}}$ |

Subtopic: Work Energy Theorem |

57%

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The figure shows the potential energy function U(x) for a system in which a particle is in a one-dimensional motion. What is the direction of the force when the particle is in region AB? (symbols have their usual meanings)

1. The positive direction of x

2. The negative direction of X

3. Force is zero, so direction not defined

4. The negative direction of y

Subtopic: Potential Energy: Relation with Force |

64%

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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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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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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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A block is carried slowly up an inclined plane. If ${\mathrm{W}}_{\mathrm{f}}$ is work done by the friction, ${\mathrm{W}}_{\mathrm{N}}$ is work done by the reaction force, ${\mathrm{W}}_{\mathrm{g}}$ is work done by the gravitational force and ${\mathrm{W}}_{\mathrm{ex}}$ is the work done by an external force, then choose the correct relation(s):

1. ${\mathrm{W}}_{\mathrm{N}}$ $+$ ${\mathrm{W}}_{\mathrm{f}}$ $+$ ${\mathrm{W}}_{\mathrm{g}}$ $+$ ${\mathrm{W}}_{\mathrm{ex}}$ $=$ $0$

2. ${\mathrm{W}}_{\mathrm{N}}$ = 0

3. ${\mathrm{W}}_{\mathrm{ex}}$ $+$ $$ ${\mathrm{W}}_{\mathrm{f}}$ $=$ $-{\mathrm{W}}_{\mathrm{g}}$

4. All of these

Subtopic: Work Energy Theorem |

70%

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