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An insect trapped in a circular groove of radius \(12\) cm moves along the groove steadily and completes \(7\) revolutions in \(100\) s. Is the acceleration vector a constant vector? What is its magnitude?

1. \(\mathrm{yes},\) \(2.3~\mathrm{cm/s^2}\)

2. \(\mathrm{no},\) \(5.3~\mathrm{cm/s^2}\)

3. \(\mathrm{yes},\) \(5.3~\mathrm{cm/s^2}\)

4. \(\mathrm{no},\) \(2.3~\mathrm{cm/s^2}\)

Subtopic: Circular Motion |

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A cricket ball is thrown at a speed of \(28\) m/s in a direction \(30^{\circ}\) above the horizontal. The maximum height attained by the ball is:

1. \(5\) m

2. \(10\) m

3. \(15\) m

4. \(20\) m

Subtopic: Projectile Motion |

77%

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An insect trapped in a circular groove of radius \(12\) cm moves along the groove steadily and completes \(7\) revolutions in \(100\) s. What is the angular speed of the motion?

1.\(0.62\) rad/s

2.\(0.06\) rad/s

3. \(4.40\) rad/s

4. \(0.44\) rad/s

Subtopic: Circular Motion |

70%

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A cricket ball is thrown at a speed of \(28\) m/s in a direction \(30^\circ\) above the horizontal. The time taken by the ball to return to the same level is:

1. \(2.5\) s

2. \(2.9\) s

3. \(3.5\) s

4. \(3\) s

Subtopic: Projectile Motion |

85%

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A hiker stands on the edge of a cliff \(490~\mathrm{m}\) above the ground and throws a stone horizontally with an initial speed of \(15\) m/s. Neglecting air resistance, the time taken by the stone to reach the ground and the speed with which it hits the ground are, respectively: (Take \(g=9.8~\mathrm{m/s^2}\))

1. | \(10\) s and \(99\) m/s |

2. | \(10\) s and \(15\) m/s |

3. | \(5\) s and \(99\) m/s |

4. | \(5\) s and \(15\) m/s |

Subtopic: Projectile Motion |

70%

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Galileo, in his book **T****wo new sciences**, stated that for elevations that exceed or fall short of \(45^\circ\) by equal amounts, the ranges:

1. | are equal to each other. |

2. | are not equal to each other. |

3. | are sometimes equal and sometimes not equal to each other. |

4. | depends on the difference between the angles. |

Subtopic: Projectile Motion |

79%

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Rain is falling vertically with a speed of \(35\) m/s. A woman rides a bicycle with a speed of \(12\) m/s in the east-to-west direction. What is the direction in which she should hold her umbrella?

1. | in the vertical direction only. |

2. | \(19^\circ\) with vertical towards east. |

3. | \(19^\circ\) with vertical towards the west. |

4. | \(19^\circ\) with vertical towards the south. |

Subtopic: Relative Motion |

56%

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A particle starts from the origin at t = 0 with a velocity of 5.0î m/s and moves in the x-y plane under the action of a force that produces a constant acceleration of (3.0î +2.0 ĵ ) $\mathrm{m}/{\mathrm{s}}^{2}$. What is the speed of the particle at the instant its x-coordinate is 84 m?

1. | 36 m/s | 2. | 26 m/s |

3. | 1 m/s | 4. | 0 m/s |

Subtopic: Uniformly Accelerated Motion |

70%

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The position of a particle is given by; \(\vec{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})\) m $\stackrel{}{\mathrm{}}$

where \(t\) is in seconds and the coefficients have the proper units for \(r\) to be in meters. The magnitude and direction of \(\vec{v}(t)\) at \(t=1.0\) s are:

1. | \(4\) m/s \(53^\circ\) with x-axis |

2. | \(4\) m/s \(37^\circ\) with x-axis |

3. | \(5\) m/s \(53^\circ\) with y-axis |

4. | \(5\) m/s \(53^\circ\) with x-axis |

Subtopic: Speed & Velocity |

66%

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A motorboat is racing towards the north at 25 km/h and the water current in that region is 10 km/h in the direction of 60° east of the south. The resultant velocity of the boat is:

1. 12 km/h at $23.{4}^{o}$ east of west

2. 22 km/h at $23.{4}^{o}$ north of east

3. 22 km/h at $23.{4}^{o}$ east of north

4. 20 km/h at $23.{4}^{o}$ north of wast

Subtopic: Relative Motion |

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