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

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

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

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

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

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%

From NCERT

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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. $\left(\frac{6}{5},\frac{6}{5}\right)$

2. $\left(\frac{1}{5},\frac{6}{5}\right)$

3. $\left(\frac{5}{6},\frac{5}{6}\right)$

4. Can't be determined

Subtopic: Center of Mass |

71%

From NCERT

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

1. $2\hat{\mathrm{i}}+12\hat{\mathrm{j}}+10\hat{\mathrm{k}}$

2. 0

3. $2\hat{\mathrm{i}}-12\hat{\mathrm{j}}-10\hat{\mathrm{k}}$

4. $2\hat{\mathrm{i}}+12\hat{\mathrm{j}}-10\hat{\mathrm{k}}$

Subtopic: Torque |

64%

From NCERT

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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 N

2. 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 |

59%

From NCERT

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

1. 30.4 N and 198 N

2. 199 N and 30 N

3. 30 N and 199 N

4. 34.6 N and 199 N

Subtopic: Torque |

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

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

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

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

4. $\frac{{\mathrm{MR}}^{2}}{4}$

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%

From NCERT

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