Center of Mass as an average point

Q.

One end of a thin uniform rod of length $L$ and mass $M_1$ is rivetted to the centre of a uniform circular disc of radius $r$ and mass $M_2$, so that both are coplanar. The distance of centre of mass of the combination from the centre of the disc is

1. $\frac{L(M_1+M_2)}{2M_1}$

2. $\frac{L{M}_1}{2(M_1+M_2)}$

3. $\frac{2(M_1+M_2)}{L{M}_1}$

4. $\frac{2L{M}_1}{(M_1+M_2)}$

Q.

The average weight of $8$ persons increases by $2.5kg$ when a new person comes in place of one of them weighing$65kg$. What might be the weight of the new person ?

1. $76kg$

2. $85kg$

3. $76.5kg$

4. Data inadequate

Q.

Four particles of masses m, m, 2m and 2m are placed at the four corners of a square of side a as shown in the figure. The (x, y) coordinates of the centre of mass are

1. $(\frac{a}{2},2a)$

2. $(\frac{a}{2},a)$

3. $(\frac{a}{2},\frac{2a}{3})$

4. $(a,\frac{a}{3})$

Q.

A uniform rod of length $l=100cm$ is bent at its mid-point to make ${90}^{\circ }$ angle. The distance of the centre of mass from the centre of the rod is

1. 36.1 cm

2. 25.2 cm

3. 17.7 cm

4. Zero

Q. The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

1. 76 kg
2. 80.5 kg
3. 85 kg
4. 92 kg

Q.

Four particles, each of mass m, are placed at the corners of a square of side a as shown in the figure. The position vector of the centre of mass is

1. $a(\hat{i}+\hat{j})$

2. $\frac{a}{2}(\hat{i}+\hat{j})$

3. $a(\hat{i}-\hat{j})$

4. $\frac{a}{2}(\hat{i}-\hat{j})$

Q.

Three particles, each of mass m, are placed at the corners of a right-angled triangle as shown in the figure. If OA = a and OB = b, the position vector of the centre of mass is

1. $\frac{1}{3}(a\hat{i}+b\hat{j})$

2. $\frac{1}{3}(a\hat{i}-b\hat{j})$

3. $\frac{2}{3}(a\hat{i}+b\hat{j})$

4. $\frac{2}{3}(a\hat{i}-b\hat{j})$

Q.

Three particles each of mass m, are placed at the corners of an equilateral triangle of side a, as shown in the figure. The position vector of the centre of mass is

1. $\frac{a}{2}(\hat{i}+\frac{\hat{j}}{\sqrt{3}})$

2. $\frac{a}{2}(3\hat{i}+\hat{j})$

3. $\frac{a}{2}(3\hat{i}+\sqrt{3}\hat{j})$

4. $\frac{a}{2}(3\hat{i}+\frac{\hat{j}}{\sqrt{3}})$

Q. Two frictionless pucks are connected by a rubber band.One of the pucks is projected across an air table, the rubber band tightens, and the second puck follows--in an apparantly randm way---the first puck. The center of mass of this two-particle system is located.

1. at a fixed distance from one of the pucks
2. usually , but not always , between the two pucks.
3. at a distance from one of the pucks that is a fixed ratio to the distance between the two pucks.
4. sometimes closer to one puck and sometimes closer to the other.

Q.
Where is the Center of Mass of the 3 particle system shown in above figure?

1. $X_{cm}=1.15Y_{cm}=1.5$
2. $X_{cm}=1.5Y_{cm}=1.6$
3. None of these
4. $X_{cm}=1.07Y_{cm}=1.33$

Q. What is the position of Center of Mass for irregular shaped objects?

1. At any point on the surface.
2. At the Geometric Center
3. Closer to the least Massive End.
4. Closer to the more Massive End.