Physics

Gravitation and Center of Mass

368 Questions

Gravitation and center of mass questions explore gravitational fields, planetary density, and the mechanics of celestial bodies. Test items include calculating gravitational strength on different planets and understanding the Roche Limit. This topic is essential for the physics syllabus of major competitive exams.

Gravitational fieldCenter of massPlanetary densityHill SphereSpace-time curvature

Gravitation and Center of Mass Questions

Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

The force of attraction between two unit point masses separated by a unit distance is called

  1. Gravitational potential

  2. Acceleration due to gravity.

  3. Gravitational field

  4. Universal gravitational constant.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Universal gravitational constant is the force of attraction between two bodies of unit mass and at a unit distance from each other.

Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

In the relation F= $\dfrac{G M m}{r^{2}}$, the quantity G

  1. depends on the value of g at the place of observation.

  2. is used only when the earth is one of the two masses.

  3. is greatest at the surface of the earth.

  4. is universal constant in nature.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

G is the universal gravitational constant which remains constant irrespective of the place and time. G is the force of attraction between two bodies of unit mass and unit distance apart.

Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

A body of mass $5\ kg$ is cut into two parts of masses (a) $\dfrac {m}{4}; \dfrac {3m}{4}$ (b) $\dfrac {m}{7}; \dfrac {5m}{7}$ (c) $\dfrac {m}{2}; \dfrac {m}{2}$ (d) $\dfrac {m}{5}; \dfrac {4m}{5}$. When these two pieces are kept apart by certain distance; In which case the gravitational force acting is maximum?

  1. In case a

  2. In case C

  3. In case d

  4. In case b
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Gravitation force between two masses is given by $F=\cfrac { G{ m } _{ 1 }{ m } _{ 2 } }{ { r }^{ 2 } } $

In case I:${ F } _{ 1 }=\cfrac { G\cfrac { m }{ 4 } .\cfrac { 3m }{ 4 }  }{ { r }^{ 2 } } =\cfrac { G{ m }^{ 2 } }{ { r }^{ 2 } } \times \cfrac { 1 }{ 16 } =\cfrac { G{ m }^{ 2 } }{ { r }^{ 2 } } \times 0.0625$
In case II: ${ F } _{ 2 }=\cfrac { G\cfrac { m }{ 7 } .\cfrac { 5m }{ 7 }  }{ { r }^{ 2 } } =\cfrac { G{ m }^{ 2 } }{ { r }^{ 2 } } \times \cfrac { 5 }{ 7 } =\cfrac { G{ m }^{ 2 } }{ { r }^{ 2 } } \times 0.714$
In case III: ${ F } _{ 3 }=\cfrac { G\cfrac { m }{ 2 } .\cfrac { m }{ 2 }  }{ { r }^{ 2 } } =\cfrac { G{ m }^{ 2 } }{ { r }^{ 2 } } .\cfrac { 1 }{ 4 } =\cfrac { G{ m }^{ 2 } }{ { r }^{ 2 } } \times 0.25$
${ F } _{ 2 }$ is maximum.

Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

Where is the centre of gravity of a uniform ring situated ?

  1. At the centre of ring.

  2. At the centre of semicircular ring

  3. At the centre of radius

  4. cant say
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Centre of gravity means a point from which the weight of a body or system may be considered to act. In uniform gravity it is the same as the centre of mass.For regular bodies centre of gravity lies at the centre of the body.Hence we know that there will be a centre for a uniform ring lamina.Hence this centre of the ring will be centre of gravity.

Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

The centre of mass of a system of particles is at the origin. From this we conclude that :

  1. The numberof particles on positive x-axis is equal to the number of particles on negative x-axis

  2. The total mass of the particles on positive x-axis is same as the total mass on negative x-axis

  3. The number of particles on X-axis may be equal to the number of particles on Y-axis.

  4. If there is a particle on the positive X-axis, there must be at least one particle in the negative X - axis.:
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Given :  The COM of the system  is at origin   i.e  $X = 0$
Let the position of particle of mass $m _1$ on the positive axis be  $a$.
Using       $X = \dfrac{m _1x _1+m _2x _2}{m _1+m _2}$
$\therefore$   $0 = \dfrac{m _1a+m _2x _2}{m _1+m _2}$              $\implies x _2 = -\dfrac{m _1}{m _2}a$
This implies that for a particle on the positive X axis, there must be at least one particle particle in the negative X axis.
Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

The centre of gravity of an object is ______ whether it is placed near the surface of the Earth or near the surface of the Moon.

  1. same

  2. different

  3. depend on the situation

  4. none
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Centre of mass is a point on a physical body which behaves as if the whole mass is concentrated over there. Whenever a force acts on a body it appears to be acting on the centre of mass. Whenever gravitational force is acting on a body it appears to be acting on a specific point on the body which is known as the centre of gravity.
 It usually coincides with the centre of mass. Earth being a larger planet than the moon, the gravitational force is more intense on earth as compared to the moon.
 The location of the centre of mass does not vary with the intensity of the force acting on the body. Similarly, centre of gravity does not vary with the intensity of the gravitational force acting on it.  Hence the centre of gravity on earth and moon will be the same

Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

The center of gravity of an object is 

  1. the sum of its moments divided by the weight of the specific object.

  2. the sum of its moments divided by the overall weight of the object.

  3. the sum of its moments of product of the overall weight of the object.

  4. none of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The center of gravity is defined as the ratio of sum of its moments to the total weight of the object.

Mathematically, center of gravity  $x = \dfrac{m _1 g x _1 + m _2 g x _2 +....m _n g x _n}{(m _1 + m _2 + .....m _n) g}$
$\implies$  $x = \dfrac{m _1  x _1 + m _2  x _2 +.... m _n x _n}{M}$
where overall weight of object $M = m _1 + m _2 +...m _n$

Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

Centre of gravity is the point

  1. where the weight of the object is supposed to be present or concentrated.

  2. where the weight of the object is perpendicular to the surface area of the object.

  3. where maximum no of molecules presents

  4. none of the above

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

It is a point on which behaves as if the whole weight of the body appears to be concentrated.

Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

Statement related to center of gravity that is incorrect is

  1. The center of gravity of an object is defined as the point through which its whole weight appears to act.

  2. The center of gravity is sometimes confused with the center of mass.

  3. The center of gravity always lies inside the object.

  4. For an object placed in a uniform gravitational field, the center of gravity coincides with the center of mass.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In case of a ring, the centre of gravity lies at the centre of the ring. Hence option c is the incorrect option

Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

For a bowling ball, how far apart are the center of gravity and center of mass?

  1. They are at almost exactly the same location.

  2. They are at opposite sides of the object.

  3. They are both at the surface of the object.

  4. They mean the same thing, so they're at the same location, as always.

  5. None of the other answers is correct.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Centre of mass and of gravity coincide for objects which are small as compared to the radius of the earth.

Note that they don't mean the same thing.

Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

What is the center of mass of an object?

  1. The mean position of the mass in an object.

  2. The geometric center of an object.

  3. The furthest away position of the mass in an object.

  4. The same as the center of gravity.

  5. The closest position of the mass in an object.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The mass of the body is scattered equally in all space around the centre of mass. It is closer to the heavier regions of the object and hence need not be at the geometric centre. 

Options C and E don't make sense. 
It doesn't coincide with the centre of gravity for very large bodies like mountains.

Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

If linear density of a rod of length 3 m varies as  $\lambda=2+x$, then the position of the centre of gravity of the rod is 

  1. $\dfrac{7}{3}m$
  2. $\dfrac{12}{7}m$
  3. $\dfrac{10}{7}m$
  4. $\dfrac{9}{7}m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The center of mass x_cm is calculated by the integral of (x * lambda * dx) / integral of (lambda * dx) from 0 to L. With lambda = 2 + x and L = 3, the numerator is integral from 0 to 3 of (2x + x^2) dx = [x^2 + x^3/3] from 0 to 3 = 9 + 9 = 18. The denominator is integral from 0 to 3 of (2 + x) dx = [2x + x^2/2] from 0 to 3 = 6 + 4.5 = 10.5. Thus, x_cm = 18 / 10.5 = 180 / 105 = 12 / 7.

Multiple choice physics turning effects of forces centre of gravity forces - vectors and moments acceleration due to gravity

AU the particles of a system are situated at a distance r from the origin. The distance of the centre of mass of the system from the origin is :

  1. = r
  2. $\leq \, r$
  3. $> r$
  4. $\leq 0$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The largest distance between the origin and center of mass would be 'r' when there is only one particle.
If there are more than one particle, the center of mass would be inside the circle of radius 'r' centered at the origin.
Hence option B is correct.