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The potential energy of a particle in a force field is \(U=\)$\frac{A}{{r}^{2}}-\frac{B}{r}$ where \(A\) and \(B\) are positive constants and \(r\) is the distance of the particle from the center of the field. For stable equilibrium, the distance of the particle is:

1. | \(\frac{B}{A}\) | 2. | \(\frac{B}{2A}\) |

3. | \(\frac{2A}{B}\) | 4. | \(\frac{A}{B}\) |

Subtopic: Â Potential Energy: Relation with Force |

Â 77%

From NCERT

AIPMT - 2012

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A body of mass \(1\) kg is thrown upwards with a velocity \(20\) ms^{-1}. It momentarily comes to rest after attaining a height of \(18\) m. How much energy is lost due to air friction?

(Take \(g=10\) ms^{-2})

1. \(20\) J

2. \(30\) J

3. \(40\) J

4. \(10\) J

Subtopic: Â Work Energy Theorem |

Â 87%

From NCERT

AIPMT - 2009

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What is the minimum velocity with which a body of mass \(m\) must enter a vertical loop of radius \(R\) so that it can complete the loop?

1. \(\sqrt{2 g R}\)

2. \(\sqrt{3 g R}\)

3. \(\sqrt{5 g R}\)

4. \(\sqrt{ g R}\)$\mathrm{}$

Subtopic: Â Gravitational Potential Energy |

Â 85%

From NCERT

NEET - 2016

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If a vector \(2\hat{i}+3\hat{j}+8\hat{k}\) is perpendicular to the vector \(-4\hat{i}+4\hat{j}+\alpha \hat{k},\) then the value of \(\alpha\) will be:

1. \(-1\)

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

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

4. \(1\)

Subtopic: Â Scalar Product |

Â 62%

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The angle between \(\mathrm{A}=\hat{\mathbf{i}}+\hat{\mathbf{j}}\) and \(\mathrm{B}=\hat{\mathbf{i}}-\hat{\mathbf{j}}\) is:

1. \(45^{\circ} \)

2. \(90^{\circ} \)

3. \(-45^{\circ} \)

4. \(180^{\circ}\)

1. \(45^{\circ} \)

2. \(90^{\circ} \)

3. \(-45^{\circ} \)

4. \(180^{\circ}\)

Subtopic: Â Scalar Product |

Â 78%

From NCERT

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Which of the diagrams shown in the figure most closely shows the variation in kinetic energy of the earth as it moves once around the sun in its elliptical orbit?

1. | 2. | ||

3. | 4. |

Subtopic: Â Conservation of Mechanical Energy |

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A bicyclist comes to a skidding stop in \(10\) m. During this process, the force on the bicycle due to the road is \(200\) N is directly opposed to the motion. The work done by the cycle on the road is:

1. | \(+2000\) J | 2. | \(-200\) J |

3. | zero | 4. | \(-20000\) J |

Subtopic: Â Work done by constant force |

Â 58%

From NCERT

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During an inelastic collision between two bodies, which of the following quantities always remain conserved?

1. | total kinetic energy |

2. | total mechanical energy |

3. | total linear momentum |

4. | speed of each body |

Subtopic: Â Collisions |

Â 79%

From NCERT

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Two inclined frictionless tracks, one gradual and the other steep meet at \(A\) from where two stones are allowed to slide down from rest, one on each track as shown in the figure.

Which of the following statement is correct?

1. | Both stones reach the bottom at the same time but not at the same speed. |

2. | Both the stones reach the bottom with the same speed and stone I reaches the bottom earlier than stone II. |

3. | Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I. |

4. | Both stones reach the bottom at different times and at different speeds. |

Subtopic: Â Gravitational Potential Energy |

Â 62%

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

1. \(15\) J

2. \(50\) J

3. \(10\) J

4. \(100\) J

Subtopic: Â Work Done by Variable Force |

Â 66%

From NCERT

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