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A person of mass 'm' ascends the stairs and goes up slowly through a height 'h'.

Then,

1. Work done by gravity is mgh

2. Work done by normal reaction is mgh

3. Work done by normal reaction is zero

4. Work done by gravity is stored as gravitational P.E.

Subtopic: Concept of Work |

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A block of mass \(m\) is being lowered by means of a string attached to it. The system moves down with a constant velocity. Then:

1. Work done by gravity on the block is positive.

2. Work done by F (the force of the string) on the block is negative.

3. Work done by gravity is equal in magnitude to that done by the string.

4. All of the above are true.

Subtopic: Concept of Work |

75%

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A particle is released from a height of \(S\) above the surface of the earth. At a certain height, its kinetic energy is three times its potential energy. The distance from the earth's surface and the speed of the particle at that instant are respectively:

1. | \({S \over 2},{ \sqrt{3gS} \over 2}\) | 2. | \({S \over 4}, \sqrt{3gS \over 2}\) |

3. | \({S \over 4},{ {3gS} \over 2}\) | 4. | \({S \over 4},{ \sqrt{3gS} \over 3}\) |

Subtopic: Gravitational Potential Energy |

69%

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A block is released from rest from a height of h = 5 m. After travelling through the smooth curved surface, it moves on the rough horizontal surface through a length l = 8 m and climbs onto the other smooth curved surface at a height h'. If $\mathrm{\mu}$ = 0.5, find h'.

1. | 2 m | 2. | 3 m |

3. | 1 m | 4. | Zero |

Subtopic: Work Energy Theorem |

64%

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The potential energy of a particle of mass m varies as the magnitude of the $U=a{x}^{2}+by.$ The magnitude of the acceleration of the particle at (0, 3) is: (symbols have their usual meaning)

1. $\sqrt{\frac{\mathrm{b}}{\mathrm{m}}}$

2. $\sqrt{\frac{3\mathrm{b}}{\mathrm{m}}}$

3. $\frac{\mathrm{b}}{\mathrm{m}}$

4. Zero

Subtopic: Potential Energy: Relation with Force |

64%

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A particle of mass 10 kg moves with a velocity of $10\sqrt{x}$ SI units, where x is displacement. The work done by the net force during the displacement of the particle from x = 4 m to x = 9 m is:

1. | 1250 J | 2. | 1000 J |

3. | 3500 J | 4. | 2500 J |

Subtopic: Work Energy Theorem |

74%

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A rigid body of mass \(\mathrm{m}\) is moving in a circle of radius \(\mathrm{r}\) with constant speed \(\mathrm{v}.\) The force on the body is $\frac{{\mathrm{mv}}^{2}}{\mathrm{r}}$ and is always directed towards the center. The work done by this force in moving the body over half the circumference of the circle will be:

1. $\frac{{\mathrm{mv}}^{2}}{\mathrm{r\pi}}$

2. ${\mathrm{mr}}^{2}\mathrm{\pi}$

3. zero

4. $2{\mathrm{mv}}^{2}\mathrm{\pi}$

Subtopic: Concept of Work |

73%

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The kinetic energy of a body is increased by 21%. The percentage increase in the magnitude of linear momentum of the body will be:

1. 10%

2. 20%

3. Zero

4. 11.5%

Subtopic: Concept of Work |

62%

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If a stone is projected vertically upward from the ground at a speed of 10 m/s, then it's: (g = 10 $\mathrm{m}/{\mathrm{s}}^{2}$)

1. Potential energy will be maximum after 0.5 s

2. Kinetic energy will be maximum again after 1 s

3. Kinetic energy = potential energy at a height of 2.5 m from the ground

4. Potential energy will be minimum after 1 s

Subtopic: Conservation of Mechanical Energy |

67%

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A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter AB = D. The height h is equal to:

1. $\frac{3}{2}D$

2. D

3. $\frac{7}{4}D$

4. $\frac{5}{4}D$

Subtopic: Conservation of Mechanical Energy |

72%

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