Intuition for COM

Q. Consider a rectangular plate of dimensions $a\times b$. If the plate is considered to be made up of four rectangles of dimensions $\frac{a}{2}\times \frac{b}{2}$ and we now remove one (the lower right) out of the four rectangles, find the position where the centre of mass of the remaining system will be (considering the center of the rectangular plate as the origin)

1. $\frac{a}{12},\frac{-b}{12}$
2. $\frac{-a}{12},\frac{-b}{12}$
3. $\frac{-a}{12},\frac{b}{12}$
4. $\frac{a}{12},\frac{b}{12}$

Q. Two balls, B and C are placed at a certain distance from each other as shown. The masses of B and C are ‘25M’ and ‘9M’ respectively. ​ Where should a third ball of mass ‘M’ be placed, so that it experiences a zero net force?

1. S
2. R
3. P
4. Q

Q. A light string passing over a smooth light pulley connects two blocks of masses M1 and M2. If the acceleration of the system is g/8, then the ratio of masses is ? Consider M1> M2

Q.

lf all the particles of a system lie in X-Y plane, is it necessary that the centre of mass be in X-Y plane?

1. Never

2. Some times

3. Not theoretically but practically

4. Yes

Q.

Four particles, each of mass m, are placed at the corners of a square of side a in the x-y plane. If the origin of the coordinate system is taken at the point of intersection of the diagonals of the square, the coordinates of the centre of mass of the system are

1. (-a, a)

2. (a, -a)

3. (0, 0)

4. (a, a)

Q. A 10kg mass moves along X-axis. Its acceleration as a functions of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from x=0 to x=8cm?

1. $8\times {10}^{-2}J$
2. $16\times {10}^{-2}J$
3. $4\times {10}^{-4}J$
4. $1.6\times {10}^{-3}J$

Q.

Four particles $A$, $B$, $C$ and $D$ having masses $m$, $2m$, $3m$ and $4m$ respectively are placed in order at the corners of a square of side $a$. Locate the centre of mass

1. ,

2. None of these

3. 

4. ,

Q.

Four particles of masses 1 kg, 2 kg, 3 kg and 4 kg are placed at the corners of a square of side 2 m in the x-y plane as shown in the figure. If the origin of the coordinate system is taken at the mass of 1 kg, the (x, y) co-ordinates of the centre of mass are

1. $(1m,\frac{7}{5}m)$

2. $(2m,\frac{7}{5}m)$

3. $(3m,\frac{7}{5}m)$

4. $(4m,\frac{7}{5}m)$

Q. In the CO molecule, the centre of mass is at a distance of 0.068 nm from the carbon atom. The separation between the nuclei of carbon and oxygen is

1. 
2. 
   
3. 
   
4. 

Q. The centre of mass of a system of two particles of masses $m_1$ and $m_2$ is at a distance $a_1$ from mass $m_1$ and at a distance $a_2$ from mass $m_2$ such that

1. 
   
2. 
3. 
4. 
   

Q. A cubical body of side 10cm each is floating into water. When 10gm mass is placed on the body, then calculate the length of body further immersed into the water due to this mass.

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

1. 
   
2. 
   
3. 
4. 
   
   

Q. Calculate the height to which liquid will rise in a capillary tube of radius ${10}^{-2}m$. Surface tension of liquid is $0.1N/m$. Angle of contact is ${60}^{\circ }$ & density of liquid is $2000{\text{kg/m}}^3$.

1. $4\times {10}^{-4}m$
2. $5\times {10}^{-4}m$
3. $4.5\times {10}^{-4}m$
4. $3\times {10}^{-4}m$

Q.

Look at the drawing given in the figure, Which has been drawn with ink of uniform line thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments is m. The mass of the ink used to draw the outer circle is 6m. The coordinates of the centres of the different parts are : outer circle (0, 0), left inner circle (-a, a), right inner circle (a, a), vertical line (0, 0) and horizontal line (0, - a). The y – coordinate of the centre of mass of the ink in this drawing is ?

1. $\frac{a}{8}$

2. $\frac{a}{10}$

3. $\frac{a}{12}$

4. $\frac{a}{3}$

Q. Three particles of the same mass lie in the x–y plane. The (x, y) coordinates of their positions are (1, 1), (2, 2) and (3, 3) respectively. The (x, y) coordinates of the centre of mass are

1. (2, 2)
2. (4, 2)
3. (6, 6)
4. (1, 2)

Q.

Four particles, each of mass m, are placed at the corners of a square of side a in the x-y plane. If the origin of the coordinate system is taken at the point of intersection of the diagonals of the square, the coordinates of the centre of mass of the system are

1. (a, a)

2. (a, -a)

3. (-a, a)

4. (0, 0)

Q. F is gravitational force between two bodies of equal mass M. Choose force for new masses at same distance.

1. $M$ & $2M$
2. $2F$
3. $M$ & $3M$
4. $3F$
5. $2M$ & $2M$
6. $4F$

Q. A person weighs 50 kgwt in water.He displaces 40 kg water when he swims keeping his body in water.The weight he loses is

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

1. $\frac{a}{2}(3i+5j)$
2. $\frac{a}{2}(3i+j/\sqrt{3})$
3. $\frac{a}{2}(3i+j)$
4. $\frac{a}{2}(i+\frac{1}{\sqrt{3}})$