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 turning effects of forces stability and centre of mass center of mass centre of mass

The centre of mass of a body:

  1. Lies always at the geometrical center

  2. Lies always inside the body

  3. Lies always outside the body

  4. Lies within or outside the body
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The centre of mass of a body can lie within or outside the body.

For example, centre of mass of a uniform rod lies at its geometrical centre which lies within the rod whereas centre of mass of a uniform ring lies at its geometrical centre which lies outside the ring.

Multiple choice physics turning effects of forces stability and centre of mass center of mass centre of mass

A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is $\alpha R$ fromthe centre of the bigger disc. The value of $\alpha$ is

  1. $\cfrac{1}{2}$
  2. $\cfrac{1}{6}$
  3. $\cfrac{1}{4}$
  4. $\cfrac{1}{3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the negative mass method, the center of mass of the remaining part is found by subtracting the mass and moment of the smaller disc from the larger one. The calculation leads to alpha = 1/3.

Multiple choice power work and power work, energy and power physics energy and its forms

A body of mass m is projected at an angle $\displaystyle \theta $ with the horizontal with an initial velocity $\displaystyle v _{0}.$ The average power of gravitational force over the whole time of flight is

  1. $\displaystyle mg\cos \theta $
  2. $\displaystyle \frac{1}{2}mg\sqrt{u\cos \theta }$
  3. $\displaystyle \frac{1}{2}mgu\sin \theta $

  4. zero
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The projected body again comes back down. Hence the net displacement in the vertical direction will be 0.
$\therefore W=mgh=mg\times 0=0$

Multiple choice physics our solar system planets of the solar system solar system and sun introduction to solar system

The mass of a planet Jupiter is $1.9 \times 10^{27} kg$ and that of the Sun is $1.99 \times 10^{30} kg$. The mean distance of the Sun from Jupiter is $7.8 \times 10^{11} m$. The gravitational force, which the Sun exerts on Jupiter is.

  1. $4.1 \times 10^{23} N$
  2. $4.1 \times 10^{34} N$
  3. $2.2 \times 10^{23} N$
  4. $2.2 \times 10^{34} N$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using Newton's Law of Universal Gravitation, F = G * (m1 * m2) / r^2. Plugging in G = 6.67e-11, m1 = 1.9e27, m2 = 1.99e30, and r = 7.8e11, the calculation yields approximately 4.1e23 N.

Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

WEIGHTLESSNESS
An astronaut experiences weightlessness in a space satellite. It is because

  1. the gravitational force is small at that location in space.

  2. the gravitational force is large at that location in space.

  3. the astronaut experiences no gravity.

  4. the gravitational force is infinitely large at that location in space.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

An astronaut experiences weightlessness in a space satellite. It is because the astronaut experiences no gravity.

Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

Astronauts on the orbiting space station are weightless because...

  1. there is no gravity in space and they do not weigh anything.

  2. space is a vacuum and there is no gravity in a vacuum.

  3. space is a vacuum and there is no air resistance in a vacuum.

  4. None of the reasons given above are correct
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

As the astronauts are in a frame which is rotating around the earth and the centripetal acceleration on astronauts and the satellite is $same$, $g=GM/r^2$ where $r$ is the radius of the orbit. So relative to the satellite the astronauts can't exert any force on satellite so no reaction force from the satellites so they feel the condition of weightlessness.


Its same like an elevator falling from top to ground freely $cable$ broken.

So the man in the elevator and the elevator have same acceleration $g$ so the man can't exert any force on the elevator so the condition of weightlessness.

Option D is correct.

Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

In which of the following situations, you will not experience weightlessness?

  1. If you are at the center of the earth

  2. You are falling freely under gravity of the earth

  3. Inside a spacecraft which is in an orbit around the earth

  4. In a lift moving downwards with uniform velocity
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Weightlessness occurs when the normal force is zero. At the center of the Earth, gravitational force is zero, but you are not in free fall in the same sense as an orbit; however, you would experience zero weight. Wait, actually, in a lift moving with uniform velocity, the acceleration is zero, so the normal force equals your weight (mg), meaning you feel your normal weight. Therefore, you do NOT experience weightlessness in a lift moving with uniform velocity.

Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

An astronaut,inside an earth`s satellite experiences weightlessness because

  1. he is falling freely

  2. no external force is acting on it

  3. no reaction is exerted by the floor of the satellite

  4. he is far away from the earth`s surface
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

An astronaut,inside an earth`s satellite experiences weightlessness because he is falling freely.

so that the correct option is A.

Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

While orbiting around the earth in a apaceship, an astronaut experiences

  1. more weight

  2. lesser weight

  3. weightlessness

  4. nothing at all
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

  • When an astronaut is orbiting the earth, he is in a state of free fall along with the space vehicle, hence the astronaut is not able to exert his mass on its surface. This condition is called weightlessness condition.
  • Hence,option C is correct.


    • Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

    While orbiting around the earth in a spaceship, an astronaut weight becomes

    1. greater than their real weight

    2. lesser than their real weight

    3. zero

    4. infinity
    Reveal answer Fill a bubble to check yourself
    C Correct answer
    Explanation

    In a spaceship the astronaut weighs zero. Since there is no gravity in the space person feels weightless. Apart from these space is a vacuum and there is no air resistance and thus we feel weightless.

    Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

    Weightlessness in a satellite is experienced because 

    1. of inertia

    2. the gravitational force acting on the satellite is zero

    3. of centre of gravity

    4. centrifugal acceleration negates the acceleration due to gravity
    Reveal answer Fill a bubble to check yourself
    D Correct answer
    Explanation

    The satellite rotates in a circular path or elliptical path such that gravitational pull is always balanced by centrifugal force due to the rotational motion of satellite.

    Thus a body in the satellite will feel weightlessness.
    although force of gravity on a body is never zero but it is balanced by centrifugal force in  this case.
    so option D is correct.

    Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

    A man weighs $75 kg$ on the surface of the earth. His weight in a geostationary satellite is:

    1. infinity
    2. $150 kg$

    3. zero
    4. $75/2 kg$
    Reveal answer Fill a bubble to check yourself
    C Correct answer
    Explanation

    A geostationary satellite revolves around the earths with the same time period of earth's rotation, that is 24 hours.
    Since it revolves with same speed, the relative velocity is zero with respect to earth and hence any body inside a geostationary satellite doesn't feel the gravity.
    So, the weight would be equal to zero.

    Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

    The percentage increase in earth's angular velocity so that all bodies lying on the equator feel weightlessness is nearly:

    1. 17%
    2. $\dfrac{100}{17}$%

    3. 1600%

    4. 1700%
    Reveal answer Fill a bubble to check yourself
    A Correct answer
    Explanation

    Weightlessness at the equator occurs when the centripetal acceleration equals gravity: omega^2 * R = g. Current omega = sqrt(g/R). To feel weightless, omega' = sqrt(g/R). Wait, the current angular velocity is such that omega^2 * R is much smaller than g. The required increase is to make omega'^2 * R = g. The ratio omega'/omega = sqrt(g/R) / (v/R) = ... The percentage increase is approximately 17%.