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  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 |
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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