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If the equation for the displacement of a particle moving on a circular path is given by \(\theta = 2t^3 + 0.5\) where \(\theta\) is in radians and \(t\) in seconds, then the angular velocity of the particle after \(2\) sec from its start is:

1. \(8\) rad/sec

2. \(12\) rad/sec

3. \(24\) rad/sec

4. \(36\) rad/sec

Subtopic: Circular Motion |

82%

From NCERT

AIIMS - 1998

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The coordinates of a moving particle at any time \(t\) are given by \(x= \alpha t^3\) and \(y = \beta t^3\). The speed of the particle at time \(t\) is given by:

1. | \(\sqrt{\alpha^{2} + \beta^{2}}\) | 2. | \(3t \sqrt{\alpha^{2} + \beta^{2}}\) |

3. | \(3t^{2} \sqrt{\alpha^{2} +\beta^{2}}\) | 4. | \(t^{2} \sqrt{\alpha^{2} +\beta^{2}}\) |

Subtopic: Speed & Velocity |

79%

From NCERT

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At the top of the trajectory of a projectile, the directions of its velocity and acceleration are:

1. | perpendicular to each other. |

2. | parallel to each other. |

3. | inclined to each other at an angle of \(45^\circ\). |

4. | antiparallel to each other. |

Subtopic: Projectile Motion |

84%

From NCERT

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Four bodies \(P\)*, *\(Q\)*, *\(R\)* *and \(S\) are projected with equal velocities having angles of projection \(15^{\circ},\) \(30^{\circ},\)\(45^{\circ},\) and \(60^{\circ}\) with the horizontal respectively. The body having the shortest range is?

1. | \(P\) | 2. | \(Q\) |

3. | \(R\) | 4. | \(S\) |

Subtopic: Projectile Motion |

74%

From NCERT

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A stone projected with a velocity \(u\) at an angle \(\theta\) with the horizontal reaches maximum height \(H_1\). When it is projected with velocity *\(u\)* at an angle \(\frac{\pi}{2}-\theta\) with the horizontal, it reaches maximum height \(H_2\). The relation between the horizontal range of the projectile \(R\) and \(H_1\) & \(H_2\)_{ }is:

1. | \(R=4 \sqrt{H_1 H_2} \) | 2. | \(R=4\left(H_1-H_2\right) \) |

3. | \(R=4\left(H_1+H_2\right) \) | 4. | \(R=\frac{H_1{ }^2}{H_2{ }^2}\) |

Subtopic: Projectile Motion |

83%

From NCERT

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A cricketer can throw a ball to a maximum horizontal distance of \(100~\text{m}\). With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is:

1. \(100~\text{m}\)

2. \(80~\text{m}\)

3. \(60~\text{m}\)

4. \(50~\text{m}\)

Subtopic: Projectile Motion |

75%

From NCERT

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The horizontal range of a projectile is \(4 \sqrt{3}\) times its maximum height. Its angle of projection will be:

1. \(45^{\circ}\)

2. \(60^{\circ}\)

3. \(90^{\circ}\)

4. \(30^{\circ}\)

Subtopic: Projectile Motion |

74%

From NCERT

PMT - 2003

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A boat is moving with a velocity \(3\hat i + 4\hat j\) with respect to ground. The water in the river is moving with a velocity\(-3\hat i - 4 \hat j\) with respect to ground. The relative velocity of the boat with respect to water is:

1. \(8\hat j\)

2.* *\(-6\hat i-8\hat j\)

3. \(6\hat i+8\hat j\)

4. \(5\sqrt{2}\)

Subtopic: Relative Motion |

83%

From NCERT

PMT - 1998

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A river is flowing from east to west at a speed of \(5\) m/min. A man on south bank of river, capable of swimming \(10\) m/min in still water, wants to swim across the river in shortest time. He should swim:

1. | Due north |

2. | Due north-east |

3. | Due north-east with double the speed of the river |

4. | None of the above |

Subtopic: Relative Motion |

58%

From NCERT

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A man sitting in a bus travelling in a direction from west to east with a speed of \(40\) km/h observes that the rain-drops are falling vertically downwards. To another man standing on ground the rain will appear:** **

1. | To fall vertically downwards |

2. | To fall at an angle going from west to east |

3. | To fall at an angle going from east to west |

4. | The information given is insufficient to decide the direction of the rain |

Subtopic: Relative Motion |

53%

From NCERT

PMT - 1999

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