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Three particles of masses \(100~\text{g}\), \(150~\text{g}\), and \(200~\text{g}\) respectively are placed at the vertices of an equilateral triangle of a side \(0.5~\text{m}\) long. What is the position of the centre of mass of three particles?

1. \(\left(\dfrac{5}{18} , \dfrac{1}{3 \sqrt{3}}\right) \)

2. \(\left(\dfrac{1}{4} , 0\right) \)

3. \(\left(0 , \dfrac{1}{4}\right) \)

4. \(\left(\dfrac{1}{3 \sqrt{3}} , \dfrac{5}{18}\right) \)

Subtopic: Center of Mass |

78%

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Position of centre of mass of a triangular lamina as shown in the figure is:

1. at the point \(P.\)

2. at the point \(G\).

3. at the point \(L\).

4. can't be determined.

Subtopic: Center of Mass |

91%

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What is the position of centre of mass of a uniform L-shaped lamina (a thin flat plate) with dimensions as shown? The mass of the lamina is 3 kg.

1. | \(\left(\dfrac{6}{5} , \dfrac{6}{5}\right)\) | 2. | \(\left(\dfrac{1}{5} , \dfrac{6}{5}\right)\) |

3. | \(\left(\dfrac{5}{6} , \dfrac{5}{6}\right)\) | 4. | Can't be determined |

Subtopic: Center of Mass |

71%

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If the force \(7\hat i+3\hat j-5\hat k\) acts on a particle whose position vector is \(\hat i - \hat j+\hat k\), the torque of the force about the origin is?

1. \(2\hat i +12\hat j+10\hat k\)

2. zero

3. \(2\hat i -12\hat j-10\hat k\)

4. \(2\hat i +12\hat j-10\hat k\)

Subtopic: Torque |

64%

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The angular momentum about any point of a single particle moving with constant velocity:

1. | increases continuously. |

2. | decreases continuously. |

3. | first increases then decrease. |

4. | remains constant throughout the motion. |

Subtopic: Angular Momentum |

81%

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Moment of a couple:

1. | depends on the point about which you take the moments. |

2. | depends on the reference frame. |

3. | does not depend on the point about which you take the moments. |

4. | does not depend on the direction of the forces. |

Subtopic: Torque |

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A metal bar 70 cm long and 4.00 kg in mass supported on two knife edges placed 10 cm from each end. A 6.00 kg load is suspended at 30 cm from one end as shown in the figure. The reactions ${\mathrm{R}}_{1}\mathrm{and}{\mathrm{R}}_{2}$ at the knife-edges are: (Assume the bar to be of uniform cross-section and homogeneous.)

1. 43.12 N and 54.88 N2. 54.88 N and 4.312 N

3. 54.88 N and 43.12 N

4. 43.12 N and 5.488 N

Subtopic: Torque |

58%

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A \(3~\text{m}\) long ladder weighing \(20~\text{kg}\) leans on a frictionless wall. Its feet rest on the floor \(1~\text{m}\) from the wall as shown in the figure. The reaction forces of the wall and the floor respectively are:

1. | \(30.4~\text{N}\) and \(198~\text{N}\) |

2. | \(199~\text{N}\) and \(30~\text{N}\) |

3. | \(34.6~\text{N}\) and \(199~\text{N}\) |

4. | \(34.6~\text{N}\) and \(199~\text{N}\) |

Subtopic: Torque |

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The moment of inertia of a disc about one of its diameters is:

1. | \(MR^2\) | 2. | \(\dfrac{MR^2}{3}\) |

3. | \(\dfrac{2MR^2}{3}\) | 4. | \(\dfrac{MR^2}{4}\) |

Subtopic: Moment of Inertia |

84%

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The moment of inertia of a rod of mass M, length l about an axis perpendicular to it through one end is:

1. ${\mathrm{Ml}}^{2}$

2. $\frac{{\mathrm{Ml}}^{2}}{2}$

3. $\frac{{\mathrm{Ml}}^{2}}{3}$

4. Can't be determined

Subtopic: Moment of Inertia |

88%

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