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On a frictionless surface, a block of mass \(M\) moving at speed \(v\) collides elastically with another block of the same mass \(M\) which is initially at rest. After the collision, the first block moves at an angle \(\theta\) to its initial direction and has a speed \(\frac{v}{3}\). The second block’s speed after the collision will be:

1. | \(\frac{2\sqrt{2}}{3}v\) | 2. | \(\frac{3}{4}v\) |

3. | \(\frac{3}{\sqrt{2}}v\) | 4. | \(\frac{\sqrt{3}}{2}v\) |

Subtopic: Collisions |

66%

From NCERT

NEET - 2015

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The potential energy of a particle in a force field is \(U=\)$\frac{A}{{r}^{2}}-\frac{B}{r}$ where \(A\) and \(B\) are positive constants and \(r\) is the distance of the particle from the center of the field. For stable equilibrium, the distance of the particle is:

1. | \(\frac{B}{A}\) | 2. | \(\frac{B}{2A}\) |

3. | \(\frac{2A}{B}\) | 4. | \(\frac{A}{B}\) |

Subtopic: Potential Energy: Relation with Force |

77%

From NCERT

AIPMT - 2012

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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 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 |

64%

From NCERT

AIPMT - 2007

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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 |

74%

From NCERT

NEET - 2019

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A particle of mass \(m\) is driven by a machine that delivers a constant power of \(k\) watts. If the particle starts from rest, the force on the particle at time \(t\) is:

1. \( \sqrt{\frac{m k}{2}} t^{-1 / 2} \)

2. \( \sqrt{m k} t^{-1 / 2} \)

3. \( \sqrt{2 m k} t^{-1 / 2} \)

4. \( \frac{1}{2} \sqrt{m k} t^{-1 / 2}\)

Subtopic: Power |

53%

From NCERT

NEET - 2015

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Forces acting on a particle have magnitudes of 14, 7, and 7 N and act in the direction of vectors \(6\hat{i} + 2\hat{j} + 3\hat{k}\), \(3\hat{i} - 2\hat{j} + 6\hat{k}\), \(2\hat{i} - 3\hat{j} - 6\hat{k}\) respectively. The forces remain constant while the particle is displaced from point A: (2, –1, –3) to B: (5, –1, 1). The coordinates are specified in meters. The work done equal to:

1. | 75 J | 2. | 55 J |

3. | 85 J | 4. | 65 J |

Subtopic: Work done by constant force |

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A body of mass m dropped from a height h reaches the ground with a speed of 1.4$\sqrt{\mathrm{gh}}$. The work done by air drag is:

1. –0.2mgh

2. –0.02mgh

3. –0.04mgh

4. mgh

Subtopic: Work Energy Theorem |

65%

From NCERT

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A chain of length L and mass m is placed upon a smooth surface. The length of BA is (L–b). What will be the velocity of the chain when its end A reaches B?

1. \(
\sqrt{\frac{2 g \sin \theta}{L}\left(L^2-b^2\right)}
\)

2. \( \sqrt{\frac{g \sin \theta}{2 L}\left(L^2-b^2\right)}
\)

3. \( \sqrt{\frac{g \sin \theta}{L}\left(L^2-b^2\right)}\)

4. None of these

Subtopic: Conservation of Mechanical Energy |

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