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Class 11 Physics Practice Test: System of Particles and Rotational Motion - Centre of Mass
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The center of mass of a distribution of mass in space is the unique point at any given time where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration.

Class 11 Physics Practice Test: System of Particles and Rotational Motion - Centre of Mass
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25 Questions

1. Two bodies of masses 5kg and 15kg are located in the cartesian plane at (1,0) and (0,1). What is the location of their centre of mass?
2. Two particles of masses 2 kg and 3 kg are at rest and are separated by 10 m. If they move towards each other under the mutual force of attraction, they would meet at _____
3. Four objects of mass 1 kg each are placed on 4 corners of a square of side 1 m as shown in the figure. Consider “O” to be the origin. What is the position of the centre of mass?
4. Consider a hollow cubical box of uniform density half-filled with water and the other half filled with air as shown in the figure. Which of the marked points are the likely positions of the centre of mass of the system?
5. The centre of mass for an object always lies inside the object.
6. The coordinates of the centre of mass of the system shown in the figures are _____
7. Centre of mass can vary upon the application of internal force.
8. The distance between the centres of carbon and oxygen in the carbon monoxide molecules is 1.13 x 10-10 m. The distance of the centre of mass of the molecule relative to the oxygen atom is _____
9. The centre of masses of two particles with masses 2 kg and 1 kg located at (1,0,1) and (2,2,0) is located at _____
10. The coordinates of the centre of mass of objects of mass 10, 20, 30 kg are (1,1,1) m. Where should an object of mass 40 kg be placed such that the centre of mass of this new system lies at (0,0,0)?
11. For which of the following does the centre of mass lie outside the body?
12. An asteroid enters the atmosphere of the earth and breaks into two pieces. One of the pieces is larger than the other. Which of the following is true considering the centre of mass of both the pieces together?
13. Two bodies of masses 5 kg and 3 kg are moving towards each other at velocities of 3 m/s and 5 m/s, respectively. What is the velocity of their centre of mass?
14. Numerous particles in a system are placed at a distance of “D” from the origin. The position of the centre of mass will definitely be _____
15. From the figure, find out the perpendicular distance of the centre of mass of the system from side AB. ABCD is a square of side 2 m.
16. Three objects of mass 1 kg each are placed at corners of a right-angled triangle AOB as shown in the figure. Consider ‘O’ as the origin and OA = OB = 1m. Determine the position of the centre of mass of this system.
17. Consider a system on which there are external forces acting. If the vector sum of all these external forces is zero, then the centre of mass _____
18. The centre of mass of the body always lies on the line of symmetry for an object with uniform density.
19. Masses 1 kg, 1.5 kg, 2 kg, and “M” kg are situated at (2,1,1), (1,2,1), (2,-2,1) and (-1,4,3). What is the value of “M” if their centre of mass is at (1,1,3/2)?
20. A system consists of 2 particles of the same mass. Let one particle be at rest and another particle have an acceleration of “2a”. What would be the acceleration of the centre of mass of the system?
21. The velocities of three particles of masses 10 kg, 20 kg and 30 kg are 10i, 10j and 10k m/s, respectively. What is the velocity of their centre of mass?
22. A uniform free rectangular steel plate is heated from 273 to 373 kelvin. The initial area of the plate is 15 sq. cm. What is the shift of the centre of mass?
23. Two particles A and B, initially at rest, start moving towards each other under a mutual force of attraction. When the speed of A is “10 m/s” and the speed of B is “800 m/s”, what is the speed of their centre of mass?
24. Particles of masses 1 kg and 3 kg are at (2i+5j+13k) m and (-6i+4j-2k) m. What is the position of their centre of mass?
25. In the figure shown below, all the contact surfaces are perfectly smooth. “M” and “m” indicate mass. When the object of mass “m” starts sliding down due to the force of gravity, then the centre of mass will _____

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