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A force \(F\) acting on an object varies with distance \(x\) as shown below:

The force is in Newton and \(x\) is in meters. The work done by the force in moving the object from \(x = 0\) to \(x = 6\) m is:

1. | \(18.0\) J | 2. | \(13.5\) J |

3. | \(4.5\) J | 4. | \(9.0\) J |

Subtopic: Work Done by Variable Force |

91%

From NCERT

AIPMT - 2005

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A ball is thrown vertically upward. It has a speed of 10m/sec when it has reached one-half of its maximum height. How high does the ball rise? Take g = 10 m/s^{2}:

1. 5m

2. 15m

3. 10 m

4. 20 m

Subtopic: Work Energy Theorem |

71%

From NCERT

AIPMT - 2005

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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 |

55%

From NCERT

AIPMT - 1999

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A particle of mass m_{1} is moving with a velocity v_{1} and another particle of mass m_{2} is moving with a velocity v_{2}. Both of them have the same momentum, but their kinetic energies are E_{1} and E_{2} respectively. If m_{1} > m_{2} then:

1. $\frac{{\mathrm{E}}_{1}}{{\mathrm{E}}_{2}}=\frac{{\mathrm{m}}_{1}}{{\mathrm{m}}_{2}}$

2. ${\mathrm{E}}_{1}>{\mathrm{E}}_{2}$

3. ${\mathrm{E}}_{1}={\mathrm{E}}_{2}$

4. ${\mathrm{E}}_{1}<{\mathrm{E}}_{2}$

Subtopic: Concept of Work |

72%

From NCERT

AIPMT - 2004

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A stone is tied to a string of length 'l' is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed 'u'. The magnitude of the change in velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is:

1. $\sqrt{{u}^{2}-g\ell}$

2. $u-\sqrt{{u}^{2}-2g\ell}$

3. $\sqrt{2\text{}\mathrm{g}\ell}$

4. $\sqrt{2({\mathrm{u}}^{2}-\mathrm{g}\ell )}$

Subtopic: Work Energy Theorem |

From NCERT

AIPMT - 2004

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A mass of \(0.5\) kg moving with a speed of \(1.5\) m/s on a horizontal smooth surface, collides with a nearly weightless spring with force constant \(k=50\) N/m. The maximum compression of the spring would be:

1. \(0.12\) m

2. \(1.5\) m

3. \(0.5\) m

4. \(0.15\) m

Subtopic: Elastic Potential Energy |

81%

From NCERT

AIPMT - 2004

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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 |

63%

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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If the kinetic energy of a body is increased by \(300\)%, then the percentage change in momentum will be:

1. \(100\)%

2. \(150\)%

3. \(265\)%

4. \(73.2\)%

Subtopic: Concept of Work |

74%

From NCERT

AIPMT - 2002

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