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 |

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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 |

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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 |

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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 |

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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 |

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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.

From NCERT

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 |

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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

From NCERT

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 |

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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 |

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