Physics Multiple Choice Questions on “System of Particles – Centre of Mass – 1”.
1. 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 _____
a) 4/3, 2/3, 2/3
b) 2/3, 4/3, 2/3
c) 2/3, 2/3, 4/3
d) 1/3, 2/3, 2/3
Answer: a
Clarification:Sum of masses = 2+1 = 3
x-coordinate;
(2*1 + 1*2)/3 = 4/3
y-coordinate;
(2*0 + 1*2)/3 = 2/3
z-coordinate;
(2*1 + 1*0)/3 = 2/3.
2. 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?
a) 1/4, 1/4
b) 3/4, 3/4
c) 3/4, 1/4
d) 1/4, 3/4
Answer: d
Clarification: Sum of masses = 5 + 15 = 20
x-coordinate;
(5*1 + 15*0)/20 = 1/4
y-coordinate;
(5*0 + 15*1)/20 = 3/4.
3. 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)?
a) 3/2, 3/2, 3/2
b) -3/2, -3/2, -3/2
c) 3/4, 3/4, 3/4
d) -3/4, -3/4, -3/4
Answer: b
Clarification: Sum of masses = 10 + 20 + 30 + 40 = 100
Since initial centre of mass is at (1,1,1), we can assume an object of 60 kg is at (1,1,1).
x-coordinate;
(60*1 + 40*x)/100 = 0
x = -3/2
y-coordinate;
(60*1 + 40*y)/100 = 0
y = -3/2
z-coordinate;
(60*1 + 40*z)/100 = 0
z = -3/2.
4. 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)?
a) 1 kg
b) 1.5 kg
c) 2 kg
d) 2.5 kg
Answer: b
Clarification: Sum of masses = 1 + 1.5 + 2 + M = 4.5 + M
x-coordinate;
(1*2 + 1.5*1 + 2*2 – M)/(4.5 + M) = 1
4.5 + M = 7.5 – M
2M = 3
M = 1.5 kg.
5.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?
a) 1/4 (-16i + 17j + 7k) m
b) 1/4 (-8i + 17j + 7k) m
c) 1/4 (-6i + 17j + 7k) m
d) 1/4 (-6i + 17j + 5k) m
Answer: a
Clarification: Sum of masses = 1 + 3 = 4
x-coordinate;
(1*2-3*6)/4 = -16/4
y-coordinate;
(1*5 + 3*4)/4 = 17/4
z-coordinate;
(1*13-3*2)/4 = 7/4
Position of centre of mass = 1/4 (-6i + 17j + 5k) m.
6. 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 _____
a) 0.48 x 10-10 m
b) 0.64 x 10-10 m
c) 0.56 x 10-10 m
d) 0.36 x 10-10 m
Answer: a
Clarification: The location of the centre of mass from an object in a two-object system is inversely proportional to the mass of the object.
The atomic mass of oxygen = 16
The atomic mass of carbon = 12
Total atomic mass = 16 + 12 = 28
The location of centre of mass relative to oxygen atom = (1.13 x 10-10) x 12 / 28
= 0.48 x 10-10 m.
7. 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 _____
a) 6 m from 4 kg body
b) 6 m from 6 kg body
c) 4 m from 4 kg body
d) 5 m from 6 kg body
Answer: a
Clarification: The two bodies would meet at their centre of mass.
Sum of masses = 2 + 3 = 5 kg
Let us consider the 2 kg body as a reference;
The centre of mass from the 2 kg body =(3 x 10) / 5
= 6 m.
8. A ball of mass 3 kg and a ball of mass 2 kg roll towards each other on a flat surface. How far is the centre of mass from the 3 kg ball of the 2 balls are separated by 6 m?
a) 1.2 m
b) 2.4 m
c) 3.6 m
d) 4.8 m
Answer: b
Clarification: Sum of masses = 3 + 2 = 5 kg
Centre of mass from 3 kg ball = (6 x 2) / 5
= 2.4 m.
9. A uniform disc of radius R is put over another uniform disc of radius 2R of same thickness and density. The edges of the two discs touch each other. What is the position of their centre of mass?
a) at 5R/3 from the centre of the larger disc
b) at 2R/3 from the centre of the larger disc
c) at 3R/5 from the centre of the larger disc
d) at 2R/5 from the centre of the larger disc
Answer: c
Clarification:Since both discs have the same thickness and density;
M/(pi x R2 x t) = M’/((pi x 4 x R2 x t)
M = M’/4
M = Mass of a smaller disc
M’ = 4M = Mass of larger disc
Sum of masses = M + 4M = 5M
The distance of centres of discs = 3R
The distance of the centre of mass from larger disc = (3R x M)/5M
= 3R/5.
10. Three identical spheres each of radius R are placed such that their centres lie on a straight line. What is the location of their centre of mass from the centre of the first sphere?
a) R
b) 2R
c) 3R
d) 4R
Answer: b
Clarification: Distance between first and last sphere = R + 2R + R = 4R
Since the spheres are identical and lie in a straight line, the centre of mass will lie exactly in the middle.
Hence the centre of mass lies at a distance of 2R from the centre of the first sphere.
11. Centre of mass can vary upon the application of internal force.
a) True
b) False
Answer: b
Clarification: No, the centre of mass cannot vary upon the application of internal force. This is because internal force do not produce any net force. Hence the state of centre of mass in this scenario will remain unchanged.