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A block of mass \(M\) is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has a force constant value of \(k\). The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be:

1. \(Mg/k\)

2. \(2Mg/k\)

3. \(4Mg/k\)

4. \(Mg/2k\)

1. \(Mg/k\)

2. \(2Mg/k\)

3. \(4Mg/k\)

4. \(Mg/2k\)

Subtopic: Elastic Potential Energy |

70%

From NCERT

AIPMT - 2009

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Water falls from a height of \(60\) m at a rate of \(15\) kg/s to operate a turbine. The losses due to frictional forces are \(10\)% of energy. How much power is generated by the turbine? (\(g=10\) m/s^{2})

1. \(8.1\) kW

2. \(10.2\) kW

3. \(12.3\) kW

4. \(7.0\) kW

1. \(8.1\) kW

2. \(10.2\) kW

3. \(12.3\) kW

4. \(7.0\) kW

Subtopic: Power |

81%

From NCERT

AIPMT - 2008

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A shell of mass 200 g is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is:

1. 100 ms^{-1}

2. 80 ms^{-1}

3. 40 ms^{-1}

4. 120 ms^{-1}

Subtopic: Collisions |

57%

From NCERT

AIPMT - 2008

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A vertical spring with a force constant *\(k\)* is fixed on a table. A ball of mass *\(m\)* at a height *\(h\)* above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance *\(d\)*. The net work done in the process is:

1. \(mg(h+d)+\frac{1}{2}kd^2\)

2. \(mg(h+d)-\frac{1}{2}kd^2\)

3. \(mg(h-d)-\frac{1}{2}kd^2\)

4. \(mg(h-d)+\frac{1}{2}kd^2\)

Subtopic: Elastic Potential Energy |

65%

From NCERT

AIPMT - 2007

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The potential energy of a long spring when stretched by \(2\) cm is \(U\). If the spring is stretched by \(8\) cm, the potential energy stored in it is:

1. \(4U\)

2. \(8U\)

3. \(16U\)

4. \(U/4\)

Subtopic: Elastic Potential Energy |

78%

From NCERT

AIPMT - 2006

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A body of mass 3 kg is under a constant force which causes a displacement *s* in metres in it, given by the relation *s* = $\frac{1}{3}$ *t*^{2}, where *t* is in sec. Work done by the force in 2 sec is:

1. $\frac{5}{19}J$

2. $\frac{3}{8}J$

3. $\frac{8}{3}J$

4. $\frac{19}{5}J$

Subtopic: Work Done by Variable Force |

77%

From NCERT

AIPMT - 2006

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\(300 ~\text{J}\) of work is done in sliding a \(2~\text{kg}\) block up an inclined plane of height \(10~\text{m}\). Taking \(g=\) \(10\) m/*s*^{2}, work done against friction is:

1. \(200 ~\text{J}\)

2. \(100 ~\text{J}\)

3. \(\text{zero}\)

4. \(1000 ~\text{J}\)

Subtopic: Work Done by Variable Force |

71%

From NCERT

AIPMT - 2006

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Body \(\mathrm{A}\) of mass \(4m\) moving with speed \(u\) collides with another body \(\mathrm{B}\) of mass \(2m\) at rest. The collision is head-on and elastic in nature. After the collision, the fraction of energy lost by the colliding body \(\mathrm{A}\) is:

1. | \(\dfrac{5}{9}\) | 2. | \(\dfrac{1}{9}\) |

3. | \(\dfrac{8}{9}\) | 4. | \(\dfrac{4}{9}\) |

Subtopic: Collisions |

64%

From NCERT

NEET - 2019

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When an object is shot from the bottom of a long, smooth inclined plane kept at an angle of \(60^\circ\) $$with horizontal, it can travel a distance \(x_1\) along the plane. But when the inclination is decreased to \(30^\circ\) $$and the same object is shot with the same velocity, it can travel \(x_2\) distance. Then \(x_1:x_2\) will be:

1. \(1:2\sqrt{3}\)

2. \(1:\sqrt{2}\)

3. \(\sqrt{2}:1\)

4. \(1:\sqrt{3}\)

Subtopic: Conservation of Mechanical Energy |

73%

From NCERT

NEET - 2019

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A force \(F = (20 + 10 y)\) acts on a particle in the \(y\)-direction where \(F\) is in Newton and \(y\) is in meter. Work done by this force to move the particle from \(y =0\) to \(y =1\) m is:

1. \(20~\text{J}\)

2. \(30~\text{J}\)

3. \(5~\text{J}\)

4. \(25~\text{J}\)

1. \(20~\text{J}\)

2. \(30~\text{J}\)

3. \(5~\text{J}\)

4. \(25~\text{J}\)

Subtopic: Work Done by Variable Force |

75%

From NCERT

NEET - 2019

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