Introduction to gravitation - class-IX

The range of gravitational force is infinite.

According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. Therefore, the gravitational force exerted by the Sun on the Earth is equal in magnitude to the force exerted by the Earth on the Sun.

The universal gravitational constant G is approximately 6.674 * 10^-11 Nm^2/kg^2.

Any two objects attract each other with a force $F _g=\dfrac{GMm}{R^2}$ where $G$ is the gravitational constant, $M$ and $m$ the masses of the two bodies and $R$ is the distance along the line joining their centre of mass

Any two objects attract each other with a force $F _g=\dfrac{GMm}{R^2}$ where $G$ is the gravitational constant, $M$ and $m$ the masses of the two bodies and $R$ is the distance along the line joining their centre of mass

The force of gravity is the force with which the earth, moon, or other massively large object attracts another object towards itself. By definition, this is the weight of the object. All objects upon earth experience a force of gravity that is directed "downward" towards the center of the earth. So, the horizontal component of the weight of body of mass $m$ will be $0$. $Option$ $C$ is correct.

The satellite revolves around the Earth in a circular orbit when centrifugal force acting outward on the satellite is balanced by the gravitational force of the Earth. Thus, when gravitational force suddenly disappears, then only centrifugal force will be acting and velocity is tangential to the orbit and hence, the satellite will fly off tangentially. It is similar to an object tied with a string, fly off when string suddenly breaks.

Answer is A.

By Newton's Third Law and Newton's Law of Universal gravitation, the gravitational force the Earth exerts on the Moon is exactly the same as the force the Moon exerts on the Earth. 
F (Earth) = F (Moon)
However, the tidal forces are not equal - the Moon exerts a greater tidal force because tidal forces result from a difference in force across the object. Because the Earth has a greater diameter, the difference in the lunar force across the Earth will be greater than the difference that the terrestrial force exerts across the lunar diameter.

According to the law of physics, the earth attracts the apple and the apple attracts the earth with the same intensity of gravity ( according to 3rd law of dynamics). However the displacement of the two bodies is inversely to their respective masses. The earth attracts the apple i.e it falls on an apple in a billionth of a billionth of a millimeter which is impossible to see.

Gravitational force is a action distance force because it can interact with an object even they are not in physical contact with each other, yet they are able to exert a push or a pull despite their physical operation. Hence gravitational force is a action at a distance force.

Gravitational force is the weakest of all the forces because its coupling constant is small in value. Gravity cannot be felt in day to day life because of the huge universe surrounding earth. Electromagnetic force is the strongest of all  force as it deals with microscopic particles.

Gravitation is a natural phenomenon by which all things with mass are brought towards one another. It is an attractive force and behaves uniformly for all values of $r$ (distance between the two bodies).

Gravitational force by Newton's law must remain the same.

in SI system, gravitational unit of force is called kilogram force.

$1 gf = 1 g$ mass $\times$ acceleration due to gravity = $980 dyne$

A force required to produce an acceleration due to gravity of earth in a body of mass 1g,is called gram force. $\displaystyle 1gm=1g\times 980c{ m }/{ { s }^{ 2 } }$ = 980 dynes.

One kilogramme force is the force due to gravity on a mass of $1 $kilogramme or $1000 g.$

In MKS, the gravitational unit of force is kilogramme force (kgf).

In CGS, the gravitational unit of force is gramme force ($gf$).

$1 g$ force is the force due to gravity on a mass of $1 g$ or $0.001 kg$.

Definition of gravitational unit of force: A force which produces an acceleration in a body equal to acceleration due to gravity on earth, when the body has a unit mass is called gravitational unit of force.

Acceleration due to gravity is denoted by '$g$'.
A force which produces an acceleration in a body equal to acceleration due to gravity on earth, when the body has a unit mass is called gravitational unit of force.

The direction of gravitational force is towards the line joining the body and the centre of the earth.

Gravity is unipolar, attractive. So when it goes through a medium, there is no polarizing effect or polarizing forces. Thus the gravitational constant is independent of the intervening medium.

Mass = $m$

Earth is about 147.1 million kilometres (91.4 million miles) from the Sun at perihelion around January 3, in contrast to about 152.1 million kilometres (94.5 million miles) at aphelion around July 4, a difference of about 5.0 million kilometres (3.1 million miles).

1kgwt is equal to 9.8N.

1kgwt = 9.8 N
1Newton = 100000 dynes
=> 1 kgwt = 980000 dynes

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)

Newton's law of universal gravitation states F = G * (m1 * m2) / r^2. The force depends on the product of the masses, not their sum.

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

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.

The satellite is revolving around earth because the centripetal force is balanced by earth's gravitational pull.If the gravitational pull disappears, the satellite free of centripetal force. So, it will travel with its instantaneous velocity i.e. in the direction tangential to the circular path.

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.

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.

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.

If the satellite is brought to standstill $v=0$ which gives the net force on the satellite=
$F=\dfrac{GMm}{{a}^{2}} $ in the direction of the centre of the earth which earlier was providing centripetal acceleration. So the satellite will fall on the earth

Using Kepler's Third Law and the relationship between orbital periods and distances, the ratio of the masses can be derived from the given orbital data.

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.

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

For any circular motion the angular momentum is conserved as no torque is acting on it because centripetal force acts through the point of axis.

$1 kgf = 9.8 N =9.8 \times {10}^{5}dyne=980 \ times 1000 dyne=1000 \times (980dyne)=1000gf$

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

Gravitational force, $F=\cfrac { G{ M } _{ 1 }{ M } _{ 2 } }{ { R }^{ 2 } } $

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.

$E=ML^2T^{-2}\ M+ML^0T^0\ G=M^{-1}L^3T^{-2}\ J=ML^2T^{-1}$

The dimensional formula for G is M^-1 L^3 T^-2, G is independent of the medium, and the formula F = G * m1 * m2 / r^2 is correct. All statements are true.

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

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.

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