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If $x$ $=$ $3$ $-4{t}^{2}$ $+$ ${t}^{3}$, then work done in the first 4s will be:

(Mass of the particle is 3 gram)

1. 384 mJ

2. 168 mJ

3. 192 mJ

4. None of the above

Subtopic: Work Energy Theorem |

54%

From NCERT

AIPMT - 1998

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Two identical balls A and B are moving with velocity $+0.5$ $m{s}^{-1}$ and $-0.3$ $m{s}^{-1}$ respectively. If they collide head on elastically, then their velocities after collision will be:

1. $-0.3$ $m{s}^{-1}$ $and$ $0.5$ $m{s}^{-1}$

2. $+0.5$ $m{s}^{-1}$ $and$ $+$ $0.3$ $m{s}^{-1}$

3. $-0.4$ $m{s}^{-1}$ $and$ $0.3$ $m{s}^{-1}$

4. $-0.3$ $m{s}^{-1}$ $and$ $-0.4$ $m{s}^{-1}$

Subtopic: Collisions |

90%

From NCERT

AIPMT - 1998

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A ball is dropped from a height of \(5~\text m.\) If it rebounds up to a height of \(1.8~\text m,\) then the ratio of velocities of the ball after and before the rebound will be:

1. \(\frac{3}{5}\)

2. \(\frac{2}{5}\)

3. \(\frac{1}{5}\)

4. \(\frac{4}{5}\)

Subtopic: Conservation of Mechanical Energy |

76%

From NCERT

AIPMT - 1998

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The kinetic energy of a person is just half of the kinetic energy of a boy whose mass is just half of that person. If the person increases his speed by \(1~\text{m/s},\) then his kinetic energy equals to that of the boy, then the initial speed of the person was:

1. \(\left( \sqrt{2}+1 \right)~\text{m/s}\)

2. \(\left( 2+\sqrt{2} \right)~\text{m/s}\)

3. \(2\left( 2+\sqrt{2} \right)~\text{m/s}\)

4. none of the above

Subtopic: Concept of Work |

57%

From NCERT

AIPMT - 1999

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A particle projected with velocity 'u' makes an angle θ with respect to horizontal. Now it breaks in two identical parts at highest point of trajectory. If one part retraces its path, then velocity of the other part is:

1. 3u cos θ

2. 2u cos θ

3. u cos θ

4. u

Subtopic: Collisions |

From NCERT

AIPMT - 1999

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If two springs, A and B $({K}_{A}$ $=$ $2$ ${K}_{B}),$ are stretched by the same suspended weights, then the ratio of work done in stretching is equal to:

1. 1 : 2

2. 2 : 1

3. 1 : 1

4. 1 : 4

Subtopic: Elastic Potential Energy |

64%

From NCERT

AIPMT - 1999

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When a spring is subjected to 4 N force, its length is a metre and if 5 N is applied, its length is b metre. If 9 N is applied, its length will be:

1. 4b – 3a

2. 5b – a

3. 5b – 4a

4. 5b – 2a

Subtopic: Elastic Potential Energy |

70%

From NCERT

AIPMT - 1999

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The bob of a simple pendulum having length \(l,\) is displaced from the mean position to an angular position \(\theta\) with respect to vertical. If it is released, then the velocity of the bob at the lowest position will be:

1. \(\sqrt{2 g l \left(\right. 1 - \cos \theta \left.\right)}\)

2. \(\sqrt{2 g l \left(\right. 1 + \cos\theta)}\)

3. \(\sqrt{2 g l\cos\theta}\)

4. \(\sqrt{2 g l}\)

Subtopic: Work Energy Theorem |

80%

From NCERT

AIPMT - 2000

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If \(\vec{F} = (60\hat{i} + 15\hat{j}-3\hat{k})\) N and \(\vec{v} = (2\hat{i} - 4\hat{j}+5\hat{k})\) m/s, then instantaneous power is:

1. \(195\) watt

2. \(45\) watt

3. \(75\) watt

4. \(100\) watt

Subtopic: Power |

88%

From NCERT

AIPMT - 2000

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A child is sitting on a swing. Its minimum and maximum heights from the ground are \(0.75\) m and \(2\) m, respectively. Its maximum speed will be: (take \(g=10\) m/s^{2})

1. \(10\) m/s

2. \(5\) m/s

3. \(8\) m/s

4. \(15\) m/s

Subtopic: Work Energy Theorem |

76%

From NCERT

AIPMT - 2001

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