Intuition for COM

Q.

The energy required to break one bond in DNA is 10-20J. Express it in eV.

Q.

A particle of mass 10g moves along a circle pf radius 6.4 cm with a constant tangential accelaration. What is the magnitude of this accelaration if the kinetic energy of the particle becomes equal to 8×10^-4 by tye end of the second revolution after the beginning of the motion?

Q. If density p , acceleration due to gravity g and frequency v are basic quantity , find the dimension of force

Q. Two spheres $A$ and $B$ of masses $m$ and $2m$ and radii $2R$ and $R$ respectively are placed in contact as shown. The COM of the system lies

1. Inside A
2. Inside B
3. At the point of contact
4. None of these

Q. Why is the mass of a flywheel concentrated at its rims ?

Q. If the earth stops rotating, the weight of a body would increase or decrease if it is so then what is the explanation behind this??

Q.

How do you find the center of mass of a rod?

Q.

You have a bag of cotton and an iron bar, each indicating a mass of $100\mathrm{kg}$ when measured on a weighing machine. In reality, one is heavier than the other. Can you say which one is heavier and why?

Q. Three identical metal balls each of radius $r$ are placed touching each other on a horizontal surface such that an equilateral triangle is formed. When the centre of the three balls are joined, centre of mass of the system is located at

1. horizontal surface.
2. centre of one of the balls.
3. line joining centre of any two balls.
4. point of intersection of the medians of the triangle

Q. What is mechanical energy? Give two examples where a body can be said to have mechanical energy.

Q.

According to pressure equation, PV=1/3 M Vrms².

=>nRT=1/3 M Vrms²

=> T directly proportional to M Vrms²

According to mean Kinetic energy,

KE(avg)=1/2 M Vrms²

=> KE(avg) directly proportional to M Vrms²

This means.. M Vrms² directly proportional to KE(avg) T

=> M Vrms² /T = KE(avg) × proportionality constant

So this means the avg Kinetic energy is inversely proportional to Absolute Temperature. But actually KE(avg) is directly proportional to T. Please clear my doubt

Q.

The velocities of three particles of masses 20g, 30g and 50g are $10\overrightarrow{i},10\overrightarrow{j},$ and $10\overrightarrow{k}$ respectively.

​The velocity of the centre of mass of the three particles is

1. 
2. 
3. 
4. 

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.

Figure (10-E4) shows two blocks of masses m and M connected by a string passing over a pulley. The horizontal table over which the mass m slides is smooth. The pulley has a radius r and moment of inertia I about its axis and it can freely rotate about this axis. Find the acceleration of the mass M assuming that the string does not slip on the pulley.

Q. A system consists of masses $M$ and $m$ (<< $M$). The centre of mass of the system is

1. nearer to $m$.
2. at the middle.
3. nearer to $M$.
4. at the position of larger mass.

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. Three particles of masses $50\text{g},100\text{g}$ and $150\text{g}$ are placed at the vertices of an equilateral triangle of side $2\text{m}$ as shown in the figure. The $(x,y)$ co-ordinates of the centre of mass (in $\text{m})$ will be

1. $(\frac{7}{6},\frac{\sqrt{3}}{2})$
2. $(\frac{7}{12},\frac{\sqrt{3}}{4})$
3. $(\frac{7}{3},\sqrt{3})$
4. $(\frac{7}{12},\frac{\sqrt{3}}{2})$

Q. Figure shows a uniform disc of radius $R$, from which a hole of radius $R/2$ has been cut out from left of the centre and is placed on the right of the centre of the disc. Find the COM of the resulting disc.

1. $(\frac{R}{4},0)$
2. $(\frac{R}{4},\frac{R}{4})$
3. $(\frac{R}{2},\frac{R}{2})$
4. $(\frac{R}{2},0)$
   

Q.

A body will weigh more in a vacuum than in the air. Justify the statement.

Q.

State two characteristics of a moving body.

Q. At an instant t , the coordinates of a particle are x=at2, y=bt2, z=0, then its velocity at that instant when its acceleration is zero will be

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.

Define mass. Is it scalar or vector?

Q.

What affects the Centre of mass?

Q.

The force with which the earth attracts an object is called the weight of the object. Calculate the weight of the moon from the following data : The universal constant of gravitation $G=6.67\times {10}^{-11}N-m{}^2/k{g}^2,$ mass of the moon = $7.36\times {10}^{22}kg,$ mass of the earth $=6\times {10}^{24}kg$ and the distance between the earth and the moon $=3,8\times {10}^{5}km.$

Q.

What are two types the momentum?

Q. Three point masses $M_1=1.6\text{kg},M_2=2.4\text{kg}$ and $M_3=2\text{kg}$ are placed at the corners of a thin massless rectangular sheet $(1.2\text{m}\times 1.0\text{m})$ as shown in the figure below. Centre of mass of the system will be located at a point (assuming $M_1$ to be at the origin)

1. $(0.8,0.6)\text{m}$
2. $(0.6,0.8)\text{m}$
3. $(0.4,0.4)\text{m}$
4. $(0.5,0.6)\text{m}$

Q.

The direction of acceleration due to gravity is always vertically downward. State whether true or false.

1. True
2. False

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. $\frac{a_1}{a_2}=\frac{m_2}{m_1}$
   
2. $\frac{a_1}{a_2}=\frac{m_1}{m_2}$
   
3. $\frac{a_1}{a_2}=\frac{m_1}{(m_1+m_2)}$
4. $\frac{a_1}{a_2}=\frac{m_2}{(m_1+m_2)}$

Q. ntA circular disc of moment of inertia I1 is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed v1. Another disc of moment of inertiaI2 is dropped coaxially onto the rotating disc. Initially the second disc has zero angular speed. Eventually both the discs rotate with a constant angular speed v2. The energy lost by the initially rotating disc to friction is?n