Three masses are placed on the x-axis: $$300$$ g at the origin, $$500$$ g at $$x =40$$ cm, and $$400$$ g at $$x=70$$ cm. The distance of the center of mass from the origin is:

 1 $$40$$ cm 2 $$45$$ cm 3 $$50$$ cm 4 $$30$$ cm
Subtopic:  Center of Mass |
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NEET - 2012
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A uniform square plate $$ABCD$$ has a mass of $$10$$ kg. If two point masses of $$5$$ kg each are placed at the corners $$C$$ and $$D$$ as shown in the adjoining figure, then the centre of mass shifts to the mid-point of:

1. $$OH$$

2. $$DH$$

3. $$OG$$

4. $$OF$$

Subtopic:  Center of Mass |
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The coordinates of the position of masses $$m_1=7$$ gm, $$m_2=4$$ gm, $$m_3=10$$ gm are $$\vec r_1=(\hat i+5\hat j-3\hat k),$$ $$\vec r_2=(2\hat i+5\hat j+7\hat k),$$ $$\vec r_3=(3\hat i+3\hat j-\hat k)$$ respectively in cm. The position of the centre of mass of the system would be:
1. $$\left(-\frac{15}{7}, \frac{85}{17}, \frac{1}{7}\right) \text{cm}$$
2. $$\left(\frac{15}{7},-\frac{85}{17}, \frac{1}{7}\right) \text{cm}$$
3. $$\left(\frac{15}{7}, \frac{85}{21},-\frac{1}{7}\right)\text{cm}$$
4. $$\left(\frac{15}{7}, \frac{85}{21}, \frac{7}{3}\right)\text{cm}$$
Subtopic:  Center of Mass |
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The centre of the mass of $$3$$ particles, $$10$$ kg, $$20$$ kg, and $$30$$ kg, is at $$(0,0,0)$$. Where should a particle with a mass of $$40$$ kg be placed so that its combined centre of mass is $$(3,3,3)$$?
1. $$(0,0,0)$$
2. $$(7.5, 7.5, 7.5)$$
3. $$(1,2,3)$$
4. $$(4,4,4)$$

Subtopic:  Center of Mass |
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Two particles of mass, $$2$$ kg and $$4$$ kg, are projected from the top of a tower simultaneously, such that $$2$$ kg of mass is projected with a speed $$20$$ m/s at an angle $$30^{\circ}$$ above horizontal and $$4$$ kg is projected at $$40$$ m/s horizontally. The acceleration of the centre of mass of the system of two particles will be:
1. $$\frac{g}{2}$$
2. $$\frac{g}{4}$$
3. $$g$$
4. $$2g$$

Subtopic:  Center of Mass |
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Five uniform circular plates, each of diameter $$D$$ and mass $$m$$, are laid out as shown in the figure. Using the origin shown, the $$y\text-\text{coordinate}$$ of the centre of mass of the ''five–plate'' system will be:

 1 $$\frac{2D}{5}$$ 2 $$\frac{4D}{5}$$ 3 $$\frac{D}{3}$$ 4 $$\frac{D}{5}$$
Subtopic:  Center of Mass |
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A man of $$50$$ kg mass is standing in a gravity free space at a height of $$10$$ m above the floor. He throws a stone of $$0.5$$ kg mass downwards with a speed of $$2~\text{ms}^{-1}$$. When the stone reaches the floor, the distance of the man above the floor will be:
 1 $$9.9$$ m 2 $$10.1$$ m 3 $$10$$ m 4 $$20$$ m
Subtopic:  Center of Mass |
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NEET - 2010
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At $$t=0$$, the positions of the two blocks are shown. There is no external force acting on the system. Find the coordinates of the center of mass of the system at $$t=3$$ seconds:

 1 $$(1,0)$$ 2 $$(3,0)$$ 3 $$(4.5,0)$$ 4 $$(2.25,0)$$
Subtopic:  Center of Mass |
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A bomb is projected from the ground at a horizontal range of $$R$$. If the bomb explodes mid-air, then the range of its centre of mass is:
1. $$\frac{R}{2}$$
2. $$R$$
3. $$2R$$
4. $$\frac{2R}{3}$$

Subtopic:  Center of Mass |
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Three identical spheres, each of mass $$M$$, are placed at the corners of a right-angle triangle with mutually perpendicular sides equal to $$2~\text{m}$$ (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of the centre of mass.

 1 $$2( \hat{i}+ \hat{j})$$ 2 $$( \hat{i}+ \hat{j})$$ 3 $${2 \over 3}( \hat{i}+ \hat{j})$$ 4 $${4 \over 3}( \hat{i}+ \hat{j})$$
Subtopic:  Center of Mass |
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