Physics

Gravitation and Center of Mass

369 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 applications of gauss's law coulomb's law physics

At all points inside a uniform spherical shell -

  1. gravitational intensity and gravitational potential both are zero

  2. gravitational intensity and gravitational potential both are non- zero

  3. gravitational intensity is non- zero and gravitational potential both are zero

  4. gravitational intensity is zero and gravitational potential both are non-zero
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Gravity Force Inside a Spherical Shell. The net gravitational force on a point mass inside a spherical shell of mass is identically zero! Physically, this is a very important result because any spherically symmetric mass distribution outside the position of the test mass m can be build up as a series of such shells


Multiple choice

If you go into space, do you get taller?

  1. Yes, cartilage disks in your spine expand with zero gravity.

  2. Um, no way
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In microgravity, the lack of compression from Earth's gravity allows the intervertebral discs in the spine to expand, causing astronauts to temporarily grow taller.

Multiple choice geography universe and space science launching of an artificial satellites around the earth launching of satellite india’s space programmes

The International space Station is currently under construction. Eventually, simulaced earth gravity may become a reality on the space station.What would the gravitational  field through the central axis be like under these conditions?

  1. zero
  2. $0.25 g$
  3. $0.5 g$
  4. $0.75 g$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a rotating space station designed to simulate gravity, the artificial gravity is created by centrifugal force. At the central axis of rotation, the radius is zero, so the centrifugal force (and thus the simulated gravitational field) is zero.

Multiple choice botany caskets of life the cell structure cytoplasm unicellular and multicellular organisms number and shape of cells diversity and classification in animals cell parameters

A cell weighing 1 mg grows to double its initial mass before dividing into two daughter cells of equal mass. Assuming no death, at the end of 100 divisions what will be the ratio of the mass of the entire populations of these cells to that of the mass of the Earth? Assume that mass of the Earth is $10^{24}Kg$ and $2^{10}$ is approximately equal to $1000$.

  1. $10^{-28}$
  2. $10^{-3}$
  3. $1$
  4. $10^3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A cell starts at 1 mg (10^-6 kg) and divides 100 times. The total number of cells after 100 divisions is 2^100. The mass of the population is 10^-6 kg * 2^100. Given that 2^10 is approximately 10^3, 2^100 = (2^10)^10 is approximately (10^3)^10 = 10^30. Thus, total mass = 10^-6 kg * 10^30 = 10^24 kg, which matches the given mass of the Earth (10^24 kg). The ratio is therefore 1.

Multiple choice geography in search of the source of wind global pressure belts pressure belts atmospheric conditions

Atmospheric pressure generated on the earth's surfaces is due to ________.

  1. gravitational force of earth

  2. Earth revolution

  3. Earth rotation

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

Atmospheric pressure is the weight of atmosphere pushing down on itself.

Earth exerts gravitational force that tends to pull the gas molecules present in the atmosphere towards its center. This creates atmospheric pressure.

Atmospheric pressure is sometimes expressed in terms of the number of inches in a column of Mercury

Atmospheric pressure is measured with a barometer.

Multiple choice lorentz transformation and muon experiment option a: relativity physics

Box $1$ and box $2$ are identical when at rest relative to each other. An astronaut floating in intergalactic space sees the two boxes fly by from the astronaut's left to his right. Box $1$ flies by at $(0.8)c(80$% of the speed of light), and box $2$ flies by at $(0.9)c(90$% of the speed of light).
Because of relativistic effects, what is true from the point of view of the astronaut?

  1. Box $2$ is longer and taller than box $1$
  2. Box $2$ is longer and not as tall asbox $1$
  3. Box $1$ is longer and taller than box $2$
  4. Box $1$ is longer and not as tall as box $2$
  5. Box $2$ is shorter and the same height as box $1$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation
According to relativity, the ;ength of moving object parallel to the direction of motion gets shortened but the length perpendicular to the motion remains the same.
Let the rest length (parallel to the motion) and rest height of both the boxes be $L _o$ and $h _o$ respectively.
Box 1 :     $v = 0.8c$
$\therefore$ Length of box 1 observed by the astronaut        $L' _1 = L _o \sqrt{1- v^2/c^2} = L _o \sqrt{1- (0.8)^2}  =0.6L _o$

Box 2 :     $v = 0.9c$
$\therefore$ Length of box 2 observed by the astronaut        $L' _2 = L _o \sqrt{1- v^2/c^2} = L _o \sqrt{1- (0.9)^2}  =0.44L _o$

$\implies$    $L _1' > L _2'$    and  $h' _1 = h' _2 = h _o$
Hence option E is correct.

Multiple choice physics properties of a magnetic field earth - a gigantic magnet magnetic field of earth introduction to magnetic field and magnetic flux

A body of mass 100 kg falls on the earth from infinity. What will be its energy on reaching the earth? Radius of the earth is 6400 km and g = 9.8 $m/s^2$. Air friction is negligible.

  1. 6.27 x $10^9$ J
  2. 6.27 x $10^{10}$ J
  3. 6.27 x $10^{12}$ J
  4. 6.27 x $10^7$ J
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\begin{array}{l} u\widehat { i } +k\widehat { i } ={ u _{ f } }+{ k _{ f } } \ \Rightarrow 0+0=\frac { { -GMm } }{ R } +\frac { 1 }{ 2 } m{ v^{ 2 } } \ \Rightarrow \frac { 1 }{ 2 } m{ v^{ 2 } }=\frac { { GMm } }{ { R\times R } } \times R \ =mgR \ =100\times 9.8\times 6400\times 1000 \ =6272000\times 1000 \ =6.27\times { 10^{ 9 } }J \end{array}$

Hence,
option $(A)$ is correct answer.

Multiple choice physics properties of a magnetic field earth - a gigantic magnet magnetic field of earth introduction to magnetic field and magnetic flux

The value of g decreases inside the surface of Earth because

  1. A force of upward attraction is applied by the shell or earth above

  2. The shell of earth above exerts no net force

  3. The distance from the centre of the Earth decreases

  4. The density of the material at the centre of the Earth very small
Reveal answer Fill a bubble to check yourself
B,C Correct answer
Explanation

for a point inside  there is no nor force of outside shell

also
$F = \dfrac{{GMx}}{{{R^3}}}.m$        inside the surface where $x$ is distance from centre.
$\therefore$ as we go inside the distance from centre decrease
$\therefore$ $\vec g$ decrease 
hence, option $(B)$ and $(C)$ both are correct.

Multiple choice physics properties of a magnetic field earth - a gigantic magnet magnetic field of earth introduction to magnetic field and magnetic flux

The height at which the weight of a body becomes $1/16^{th}$, its weight on the surface of earth (radius R), is :-

  1. 3R

  2. 4R

  3. 5R

  4. 15R
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The acceleration due to gravity at height h is given by g_h = g * R^2 / (R + h)^2. We are given that weight (and hence g_h) becomes 1/16 of the surface value, so g / 16 = g * R^2 / (R + h)^2. Taking the square root gives 1/4 = R / (R + h), which simplifies to R + h = 4R, so h = 3R.

Multiple choice physics dynamics - explaining motion air resistance fluid friction moving through fluids

A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If$ P(r)$ is the pressure at $r(r < R)$, then the correct option(s) is(are)?

  1. $P(r=0)=0$
  2. $\dfrac{P(r=3R/4)}{P(r=2R/3)}=\dfrac{63}{80}$
  3. $\dfrac{P(r=3R/5)}{P(r=2R/5)}=\dfrac{16}{21}$
  4. $\dfrac{P(r=R/2)}{P(r=R/3)}=\dfrac{20}{27}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a fluid sphere under gravity, the pressure distribution follows hydrostatic equilibrium. Calculating the ratio of pressures at the specified radii confirms the result in option B.

Multiple choice physics types of energy law of conservation of energy the law of conservation of energy work, energy and machines

When a stone falls freely towards the earth, its total energy ?

  1. First decreases and then becomes zero

  2. Remains constant

  3. Increases

  4. Decreases
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the ball is in free-fall, the only force acting on it is gravity. Therefore, we can use the principle of conservation of mechanical energy - initially the ball has potential energy and no kinetic energy. As it falls, its total energy (the sum of the KE and the PE) remains constant and equal to its initial PE.
Hence, option B is correct.

Multiple choice biology solar equipment renewable and non-renewable resources renewable and non-renewable sources of energy production of electricity from solar energy

Density of the core of sun which is $10$ times that of gold or lead is about

  1. $100g{cm}^{-1}$
  2. ${120}g{cm}^{-1}$
  3. $150g{cm}^{-1}$
  4. $200g{cm}^{-1}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The density of the Sun's core is approximately 150 g/cm^3, which is about 150 times the density of water and significantly denser than lead or gold.

Multiple choice newton's colour disc light and the formation of shadows physics

In Newton's experiment the radii of the $m^{th}$ and $(m+4)^{th}$ dark rings are respectively $\sqrt{5}$mm and $\sqrt{7}$mm. What is the value of m?

  1. $2$
  2. $4$
  3. $8$
  4. $10$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Radius of mth dark fringe   $r _m = \sqrt{mR\lambda}$
Thus we get  $r _{m+4} = \sqrt{7} = \sqrt{(m+4)R\lambda}$     ......(1)
Also,  $r _m = \sqrt{5} = \sqrt{mR\lambda}$      .......(2)
Dividing equation (1) with equation (2),  
$ \sqrt{\dfrac {m+4}{m} }= \sqrt{\dfrac{7}{5}}$
$\dfrac{m+4}{m} = \dfrac{7}{5}$
$5(m+4)= 7m$
$5m+20= 7m$
$2m=20$
$\implies   \ m=10$