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

If the gravitational force of earth suddenly disappears, then which of the following is correct?

  1. weight of the body is zero

  2. mass of the body is zero

  3. both mass and weight become zero

  4. neither the weight nor the mass is zero
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Mass = $m$

Acceleration due to gravity = $g$
Weight of a body is given by, $(W) = m\times g$
When gravitational force disappears $g$ becomes zero, but the mass remains the same.
So, $W = m\times g=m\times 0$ 
Hence, $W = 0$
Correct option will be $(A)$

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

Two identical particles of mass m are placed at a distance r from each other. If their separation is doubled, then the effect on gravitational constant will be 

  1. Gravitational constant remains same

  2. Gravitational constant becomes quadrupled

  3. Gravitational constant becomes 1/4th the actual one

  4. Gravitational constant becomes doubled
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Gravitational constant does not depend on masses, distances between them

Changing the distance between the masses, decreases the force between them, so that $Fr^2$ remains the same

The correct option is (a)

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

The gravitational force between two points masses $m _{1}$ and $m _{2}$ at separation $r$ is given by $F=G\dfrac {m _{1}m _{2}}{r^{2}}$ The constant $G$

  1. depends on system of unit only

  2. depends on media between masses only
  3. depends on both $a$ and $b$
  4. is independent of both $a$ and $b$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The gravitational constant G is a universal constant, meaning it does not depend on the system of units or the medium between the masses.

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

At what height from the surface of the earth will the value of acceleration due to gravity be reduced by $36\%$ from the value at the surface?
(Radius of earth=$6400\ km$)

  1. $1500\ km$
  2. $1200\ km$
  3. $1000\ km$
  4. $1600\ km$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If g is reduced by 36%, the new g' = 0.64g. Using g' = g * (R / (R+h))^2, we get 0.64 = (R / (R+h))^2, so 0.8 = R / (R+h). Solving for h gives h = 0.25R = 1600 km.

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

Two balls, each of radius $R$, equal mass and density are placed in contact, than the force of gravitation between them is proportional to

  1. $F\propto \dfrac {1}{R^{2}} $
  2. $F\propto R $
  3. $F\propto R^{4} $
  4. $F\propto \dfrac {1}{R} $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given,

Two balls, each of radius $R$ and of equal mass and density, are placed in contact.

  • Step-1:

Find the Distance between the centre of two balls

Distance between the centre of two balls $=$ Sum of their Radii.

Distance between the centre of two balls $= R+R = 2R$.

  • Step-2:

Express the Mass of a ball as product of Density and Volume.

(This would be same for other ball ,given that two balls have equal mass)

Since, the shape of the ball is Sphere.

Volume of the ball $V=\dfrac 43 \pi R^3$

So,

Mass of the ball $m=\rho\times \dfrac 43 \pi R^3$

  • Step-3:

Find the force of gravitation between the two balls.

According to Newton's Law of Universal Gravitation

$F=\dfrac{GMm}{r^2}$

Where,

$F =$ Gravitational Force between two objects.

$G =$ Gravitational constant

$M =$ Mass of the first object

$m =$ Mass of the second object

$r =$ Distance between objects

Here,
.
$M=m=\rho \times \dfrac 43 \pi R^3$

Substituting Values

$\implies F=\dfrac{Gm^2}{(2R)^2}$

$\implies F=\dfrac{G(\rho \times \dfrac 43\pi R^3)^2}{4R^2}$

$\implies F=G\times \rho^2\times (\dfrac 43)^2 \times \dfrac 14\times \dfrac{R^6}{R^2}$

$\implies F=G\times \rho^2\times (\dfrac 43)^2 \times \dfrac 14 \times R^4$

$\implies F\propto R^4$

Therefore,

The force of gravitation between the two balls is proportional to $R^4$
Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

A body has a weight $90\ N$ on the earth's surface the mass of the moon is $1/9$ that of the earth's mass and its radius is $1/2$ that of the earth's radius. on the moon the weight of the body is :

  1. $45\ N$
  2. $202.5\ N$`
  3. $90\ N$
  4. $40\ N$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Weight on Moon = W_earth * (M_moon / M_earth) * (R_earth / R_moon)^2. Given M_moon = 1/9 M_earth and R_moon = 1/2 R_earth, Weight = 90 * (1/9) * (2)^2 = 10 * 4 = 40 N.

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

If the distance between two bodies is doubles, the force of gravitational attraction between them. 

  1. Becomes four times

  2. Is doubled

  3. Is reduced to one-fourth

  4. Is reduced to half.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Gravitational force is inversely proportional to the square of the distance (F proportional to 1/r^2). If distance is doubled, force becomes 1/(2^2) = 1/4 of the original.

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

Two solid spherical planets of equal radii R having masses 4 M and 9 M their centre are separated by a distance 6 R. A projectile of mass m is sent from the planet of mass 4 M towards the havier planet. what is the distance r of the point from the lighter planet where the gravitational force on the projectile is zero? 

  1. $1.4 R$
  2. $1.8 R$
  3. $1.5 R$
  4. $2.4 R$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

At the point where force is zero, the gravitational pull from both planets must be equal. G * 4M * m / r^2 = G * 9M * m / (6R - r)^2. Taking the square root: 2/r = 3/(6R - r). Solving gives 12R - 2r = 3r, so 5r = 12R, r = 2.4R.

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

Two spheres of masses $m$ and $M$ are situated in air and the gravitational force between them is $F$. The space around the masses is now filled with a liquid of specific gravity $3$. The gravitational force will now be

  1. $2 F$
  2. $F$
  3. $\displaystyle\frac {F}{3}$
  4. $\displaystyle \frac {F}{9}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The force of gravitation will be same as $F$ because gravitational force is dependent on the masses of the body and distance between them and does not depend on the medium between the masses.

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

The force acting on a mass of 1g due to the gravitational pull on the earth is called 1gwt. One gwt equals:

  1. 1 N

  2. 9.8 N

  3. 980 dyne

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

1gwt is the force acting on a mass of $1g$ due to gravitational pull on earth

$1gwt=\frac{1}{1000}Kg \times 9.8ms^{-2}$
             =$9.8\times 10^{-3}N$
$1N=10^{5}dyne$
$9.8\times 10^{-3}N=980dyne$

$1gwt=980 dyne$

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

The gravitational force with which the earth attracts the moon :

  1. is less than the force with which the moon attracts the earth

  2. is equal to the force with which the moon attracts the earth

  3. is greater than the force with which the moon attracts the earth

  4. varies with the phases of the moon
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

By the Newton's gravitational law, the gravitational force between two bodies of masses $m _1$ and $m _2$ is given by $F=-\dfrac{Gm _1m _2}{r^2}$

where $r$ be the distance between them and negative sign indicates the attraction force. 
Thus, both of them attract each other with same force.

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

The mass of the moon is about $1.2$% of the mass of the earth. Compared to the gravitational force that earth exerts on the moon, the gravitational force the moon exerts on earth :

  1. is the same

  2. is smaller

  3. is greater

  4. Varies with its plane
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The gravitation force of attraction between two bodies is given by, $F=-\dfrac{Gm _1m _2}{r^2}$ where $G=$ gravitational constant, $m _1,m _2$  be the masses of bodies and $r$ be the distance between them.

As the force depends on the product of masses and distance between them, so same force will exert on each other.