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The centre of gravity of an object is its geometric property. It is the average location of the body’s weight.
- The Centre of gravity can be defined as a point where the whole weight of the body is supposed to be concentrated.
- The motion of an object through space can be completely described by the movement of the centre of gravity of the object from one place to another.
- If the body is rotating then its motion can be described by the rotation of the object about its centre of gravity.
The centre of mass is analogous to the centre of gravity in a homogeneous gravitational field.
- The two points do not necessarily have to coincide.
- The Moon's mass centre is quite close to its geometric centre.
- However, its centre of gravity is tilted slightly towards the Earth.
- This is due to the greater gravitational force of attraction on the Moon's near side.
Very Short Answers Questions [1 Mark Questions]
Ques. What is meant by centre of gravity?
Ans. Centre of gravity is the average location of the weight of the body and it is defined as the point where the whole weight of the body is supposed to be concentrated.
Ques. The _____ is a point where mass distribution is uniform in all directions.
- Centre of gravity
- Centre of mass
- Equilibrium
- None of the above
Ans. The correct answer is b. Centre of mass
Explanation: The centre of mass is a point where mass distribution is uniform in all directions.
Ques. In the cases of irregularly shaped objects or hollow bodies, the _____ may exist in space at a point external to the physical body.
Answer: Centre of gravity
Explanation: The centre of gravity may exist in space at a place exterior to the physical body in the case of irregularly shaped objects or hollow things.
Ques. What is the connection between the centre of gravity and the centre of mass in a uniform gravitational field?
Ans. In a uniform gravitational field, the coordinates of the centre of mass are equal to the coordinates of centre of gravity.
Ques. Why is the Moon’s centre of gravity positioned towards the Earth?
Ans. Due to the heavier gravitational force field on the near side of the moon, its centre of gravity is positioned towards the Earth.
Short Answers Questions [2 Marks Questions]
Ques. What is the relationship between centre of gravity and stability?
Ans. There is a close relationship between the centre of gravity and stability. If the centre of gravity of an object is directly over its base of support, then the object is most stable. If the centre of gravity of the object moves outside the base of support, then the object becomes unstable and may fall over.
Ques. What factors affect centre of gravity?
Ans. The shape, size, and weight distribution of an object influences its centre of gravity. Objects having a greater concentration of mass towards one end will have a centre of gravity closer to that end.
Ques. How is centre of gravity determined?
Ans. The centre of gravity of a body can be determined experimentally by suspending the object from various places and locating the point where it hangs in perfect equilibrium. It may also be estimated theoretically by taking the weighted average of all the locations of an object's pieces.
Ques. What is the relationship between the centre of gravity and the geometric centre of a body?
Ans. In a symmetrically configured body made of homogeneous material, the position of the centre of gravity coincides with the geometric centre of the body. However, for irregularly shaped objects or having non-uniform mass distribution, the position centre of gravity and geometric centre does not coincide.
Check More:
| Relevant Articles | ||
|---|---|---|
| Gravitational Potential Energy | Value of g on Moon | Newton's Laws of Motion |
| Force of Attraction Formula | Force and Laws of Motion | Gravity Waves |
Long Answers Questions [3 Marks Questions]
Ques. What effect does the Center of Gravity have on the balance?
Ans. The centre of gravity of an object influences its stability.
- The lower the centre of gravity of an object, the more stable it is.
- The higher the object, the more likely it is to collapse if pushed.
- Racing cars have a low centre of gravity, which allows them to turn rapidly without toppling over.
Ques. What is the difference between centre of mass and centre of gravity?
Ans. The followings are the differences between the centre of mass and centre of gravity
| Centre of mass | Centre of gravity |
|---|---|
| It is defined as the point at which the distribution of mass is uniform in all directions. | It is defined as the point at which weight is evenly distributed in all directions. |
| It is the point where all the mass of a body is supposed to be concentrated. | It is the point where all the weight of a body is supposed to be concentrated. |
| It is based on the mass of the body | It is based on the weight of the body |
| When a body moves across an axis, the mass on the left side equals the mass on the right side. | When a body moves across an axis, the weight on the left side equals the weight on the right side. |
Ques. How is centre of Gravity used in sports and recreation?
Ans. Understanding the centre of gravity is essential for maintaining balance and stability in sports and recreation. For example, snowboarders, skiers, and skateboarders change their body posture to keep their centre of gravity over their base of support, allowing them to stay upright and perform their tricks.
Very Long Answer Questions [5 Marks Questions]
Ques. The coordinates of vertices of a triangle ABC are A(1, 2), B(4, 6), and C(-3, -2). Three particles of masses 1 kg, 2 kg, and m kg are placed at the vertices of the triangle. If the coordinates of centre of gravity are (3/5, 2). Find the mass m.
Ans. Let the coordinates of centre of gravity be (x, y), then for three particle system
x = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3) and
y = (m1y1 + m2y2 + m3y3) / (m1 + m2 + m3)
Given
- x = 3/5 and y = 2
- x1 = 1, x2 = 4, and x3 = – 3
- y1 = 2, y2 = 6, and y3 = – 2
- m1 = 1 kg, m2 = 2 kg, and m3 = m
On substituting the values in x coordinate, we get
x = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3)
⇒ 3/5 = (1 x 1 + 2 x 4 + 3 x -3) / (1 + 2 + m)
⇒ 3/5 = (9 - 3m) / (3 + m)
⇒ 9 + 3m = 45 - 15m
⇒ m = 2 kg
Ques. Two bodies of masses 1 kg and 2 kg are lying in the x-y plane at (-1, 2) and (2, 4) respectively. What are the coordinates of centre of gravity?
Ans. Let the coordinates of centre of gravity be (x, y), then for two particle system
x = (m1x1 + m2x2) / (m1 + m2) and
y = (m1y1 + m2y2) / (m1 + m2)
Given
- x1 = -1 and y1 = 2
- x2 = 2, and y2 = 4
- m1 = 1 kg
- m2 = 2 kg
On substituting the values in x coordinate, we get
x = (m1x1 + m2x2) / (m1 + m2)
⇒ x = (1 x -1 + 2 x 2) / (1 + 2)
⇒ x = 1
On substituting the values in the y coordinate, we get
y = (m1y1 + m2y2) / (m1 + m2)
⇒ y = (1 x 2 + 2 x 4) / (1 + 2)
⇒ y = 10/3
Therefore, the coordinates of centre of gravity are (1, 10/3)
Ques. Three bodies of masses 1 kg, 2 kg, and 3 kg are lying in the x-y plane at (0, 0), (2, 2), and (4, 0) respectively. What are the coordinates of centre of gravity?
Ans. Let the coordinates of centre of gravity be (x, y), then for three particle system
x = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3) and
y = (m1y1 + m2y2 + m3y3) / (m1 + m2 + m3)
Given
- x1 = 0, x2 = 2, and x3 = 4
- y1 = 0, y2 = 2, and y3 = 0
- m1 = 1 kg, m2 = 2 kg, and m3 = 3 kg
On substituting the values in x coordinate, we get
x = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3)
⇒ x = (1 x 0 + 2 x 2 + 3 x 4) / (1 + 2 + 3)
⇒ x = 8/3
On substituting the values in y coordinate, we get
y = (m1y1 + m2y2 + m3y3) / (m1 + m2 + m3)
⇒ x = (1 x 0 + 2 x 2 + 3 x 0) / (1 + 2 + 3)
⇒ x = 2/3
Therefore, the coordinates of centre of gravity are (8/3, 2/3).
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