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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 |

52%

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 |

89%

From NCERT

AIPMT - 1998

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A ball is dropped from a height of \(5\) m. If it rebounds up to a height of \(1.8\) 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 |

74%

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 |

54%

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 |

62%

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 |

69%

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 θ with respect to vertical. If it is released, then the velocity of the bob at the lowest position will be:

1. $\sqrt{2gl(1-\mathrm{cos}\theta )}$

2. $\sqrt{2gl(1+\mathrm{cos}}$ $\theta )$

3. $\sqrt{2gl}$ $\mathrm{cos}\theta $

4. $\sqrt{2gl}$

Subtopic: Work Energy Theorem |

79%

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 |

87%

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 |

74%

From NCERT

AIPMT - 2001

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