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Consider the motion of the tip of the second hand of a clock. In one minute (assuming \(R\) to be the length of the second hand), its:

1. | displacement is \(2\pi R\) |

2. | distance covered is \(2R\) |

3. | displacement is zero. |

4. | distance covered is zero. |

Subtopic: Position & Displacement |

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A person, reaches a point directly opposite on the other bank of a flowing river, while swimming at a speed of \(5\) m/s at an angle of \(120^\circ\) with the flow. The speed of the flow must be:

1. \(2.5\) m/s

2. \(3\) m/s

3. \(4\) m/s

4. \(1.5\) m/s

Subtopic: Relative Motion |

83%

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When a particle is projected at some angle to the horizontal, it has a range \(R\) and time of flight \(t_1\). If the same particle is projected with the same speed at some other angle to have the same range, its time of flight is \(t_2\), then:

1. \(t_{1} + t_{2} = \frac{2 R}{g}\)

2. \(t_{1} - t_{2} = \frac{R}{g}\)

3. \(t_{1} t_{2} = \frac{2 R}{g}\)

4. \(t_{1} t_{2} = \frac{R}{g}\)

Subtopic: Projectile Motion |

74%

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A car is moving at a speed of \(40\) m/s on a circular track of radius \(400\) m. This speed is increasing at the rate of \(3\) m/s^{2}. The acceleration of the car is:

1. \(4\) m/s^{2}

2. \(7\) m/s^{2}

3. \(5\) m/s^{2}

4. \(3\) m/s^{2}

Subtopic: Circular Motion |

75%

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A particle starts from the origin at \(t=0\) sec with a velocity of \(10\hat j~\text{m/s}\) and moves in the \(x\text-y\) plane with a constant acceleration of \((8.0\hat i +2.0 \hat j)~\text{m/s}^2\). At what time is the \(x\text-\)coordinate of the particle \(16~\text{m}\)?

1. \(2\) s

2. \(3\) s

3. \(4\) s

4. \(1\) s

Subtopic: Uniformly Accelerated Motion |

72%

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Three girls skating on a circular ice ground of radius \(200\) m start from a point \(P\) on the edge of the ground and reach a point \(Q\) diametrically opposite to \(P\) following different paths as shown in the figure. The correct relationship among the magnitude of the displacement vector for three girls will be:

1. \(A > B > C\)

2. \(C > A > B\)

3. \(B > A > C\)

4. \(A = B = C\)

Subtopic: Position & Displacement |

84%

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A cat is situated at point \(A\) (\(0,3,4\)) and a rat is situated at point \(B\) (\(5,3,-8\)$\mathrm{}$). The cat is free to move but the rat is always at rest. The minimum distance travelled by the cat to catch the rat is:

1. \(5\) unit

2. \(12\) unit

3. \(13\) unit

4. \(17\) unit

Subtopic: Position & Displacement |

75%

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Two bullets are fired simultaneously horizontally and at different speeds from the same place. Which bullet will hit the ground first? (Air resistance is neglected)

1. | The faster one |

2. | The slower one |

3. | Depends on masses |

4. | Both will reach simultaneously |

Subtopic: Projectile Motion |

76%

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A bus is going to the North at a speed of \(30\) kmph. It makes a \(90^{\circ}\) left turn without changing the speed. The change in the velocity of the bus is:

1. | \(30\) kmph towards \(W\) |

2. | \(30\) kmph towards \(S\text-W\) |

3. | \(42.4\) kmph towards \(S\text-W\) |

4. | \(42.4\) kmph towards \(N\text-W\) |

Subtopic: Speed & Velocity |

58%

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A man can row a boat with a speed of \(10\) kmph in still water. The river flows at \(6\) kmph. If he crosses the river from one bank to the other along the shortest possible path, time taken to cross the river of width \(1\) km is:

1. \(\frac{1}{8}~\text{h}\)

2. \(\frac{1}{4}~\text{h}\)

3. \(\frac{1}{2}~\text{h}\)

4. \(1~\text{h}\)

Subtopic: Relative Motion |

72%

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