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A uniform square plate \(ABCD\) has a mass of \(10\) kg.
If two point masses of \(5\) kg each are placed at the corners \(C\) and \(D\) as shown in the adjoining figure, then the centre of mass shifts to the mid-point of:

1. \(OH\)

2. \(DH\)

3. \(OG\)

4. \(OF\)

Subtopic: Center of Mass |

83%

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The mass per unit length of a non-uniform rod of length \(L\) is given by \(\mu =λx^{2}\) where \(\lambda\) is a constant and \(x\) is the distance from one end of the rod.
The distance between the centre of mass of the rod and this end is:

1. \(\frac{L}{2}\)

2. \(\frac{L}{4}\)

3. \(\frac{3L}{4}\)

4. \(\frac{L}{3}\)

Subtopic: Center of Mass |

71%

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The centre of the mass of \(3\) particles, \(10\) kg, \(20\) kg, and \(30\) kg, is at \((0,0,0)\). Where should a particle with a mass of \(40\) kg be placed so that its combined centre of mass is \((3,3,3)\)?

1. \((0,0,0)\)

2. \((7.5, 7.5, 7.5)\)

3. \((1,2,3)\)

4. \((4,4,4)\)

Subtopic: Center of Mass |

76%

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Five uniform circular plates, each of diameter \(D\) and mass \(m\), are laid out as shown in the figure. Using the origin shown, the \(y\text-\text{coordinate}\) of the centre of mass of the ''five–plate'' system will be:

1. | \(\frac{2D}{5}\) | 2. | \(\frac{4D}{5}\) |

3. | \(\frac{D}{3}\) | 4. | \(\frac{D}{5}\) |

Subtopic: Center of Mass |

75%

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A man of \(50\) kg mass is standing in a gravity free space at a height of \(10\) m above the floor. He throws a stone of \(0.5\) kg mass downwards with a speed of \(2~\text{ms}^{-1}\). When the stone reaches the floor, the distance of the man above the floor will be:

1. | \(9.9\) m | 2. | \(10.1\) m |

3. | \(10\) m | 4. | \(20\) m |

Subtopic: Center of Mass |

74%

From NCERT

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At \(t=0\), the positions of the two blocks are shown. There is no external force acting on the system. Find the coordinates of the center of mass of the system at \(t=3\) seconds:

1. | \((1,0)\) | 2. | \((3,0)\) |

3. | \((4.5,0)\) | 4. | \((2.25,0)\) |

Subtopic: Center of Mass |

74%

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Three identical spheres, each of mass \(M\), are placed at the corners of a right-angle triangle with mutually perpendicular sides equal to \(2~\text{m}\) (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of the centre of mass.

1. | \(2( \hat{i}+ \hat{j})\) | 2. | \(( \hat{i}+ \hat{j})\) |

3. | \({2 \over 3}( \hat{i}+ \hat{j})\) | 4. | \({4 \over 3}( \hat{i}+ \hat{j})\) |

Subtopic: Center of Mass |

71%

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A boat of length \(10\) m and a mass of \(450\) kg is floating without motion in still water. A man of \(50\) kg standing at one end walks to the other end and comes to a stop. The magnitude of the displacement of the boat relative to the ground is:

1. | zero | 2. | \(1\) m |

3. | \(2\) m | 4. | \(5\) m |

Subtopic: Center of Mass |

63%

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A wheel has an angular acceleration of \(3.0\) rad/s^{2} and an initial angular speed of \(2.00\) rad/s. In a time of \(2\) s,
it has rotated through an angle (in radian) of:

1. \(6\)

2. \(10\)

3. \(12\)

4. \(4\)

Subtopic: Rotational Motion: Kinematics |

87%

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If a body is moving in a circular path with decreasing speed, then: (symbols have their usual meanings):

1. $\overrightarrow{r}.\overrightarrow{\omega}$ $=$ $$ $0$

2. $\overrightarrow{\tau}.\overrightarrow{v}$ $=$ $0$

3. $\overrightarrow{a}.\overrightarrow{v}$ $<$ $0$

4. All of these

Subtopic: Rotational Motion: Kinematics |

68%

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