JKBOSE 9th Class Science Solutions Chapter 4 Gravitation 

◆ Everybody in this universe attracts every other body towards it with a force called Force of Gravitation.

◆ The revolution of the moon around the earth and the falling down of a body projected upward is due to force of gravitation.

◆ Gravitation is a weak force unless it may not involve bodies having greater masses.

◆ The attractive force due to earth is called force of gravity.

◆ Law of gravitation states that the force of attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of distance between their centres.

This force always acts along the line joining the centres of two objects.

◆ The law of gravitation is a universal law which means that this law applies to all minha Jisko big and small objects.

◆ The magnitude of the force acting between the earth and the objects lying on the surface of earth is given by formula F =  GMm / d² where G = 6.673 × 10^-11 N – m²/kg²

◆ The acceleration produced in the body due to force of gravity is called acceleration due to gravity. It is denoted by ‘g’.

◆ The value of ‘g’ is more on the poles than on the equatorial line.

◆ Force of gravity decreases with the increase of height above the surface of earth.

◆ Kepler gave the following three laws which govern the motion of the planets :

(i) The planetary path of each planet is elliptical at the centre of which the sun ad is situated.

(ii) The line joining sun and the planet sweeps equal area in equal interval of time.

(iii) The cube of average distance ‘r’ of a planet from the sun is inversely proportional to the square of the orbital period ‘T’ of that planet.

◆ The quantity of matter present in an body is called the mass of the body. Mass is the measure of inertia of the body. The mass of a body remains constant at all places.

◆ The weight of a body is the force with which the body is attracted towards the centre of the earth

⇒ Force of Gravitation. It is that force with which two bodies attract each other but they are lying apart.

⇒ Universal law of Gravitation. The mutual force of attraction between every two bodies in this universe is directly proportional to the product of the masses of the two bodies and inversely proportional to the square of the distance between them. This force acts along the line joining the centres of the two bodies.

⇒ Acceleration due to Gravity. Acceleration produced in the bodies falling freely under the action of gravity is called acceleration due to gravity.

⇒ Force of Gravity. It is the force with which earth attracts all bodies towards its centre.

⇒ Weight. The force with which the earth attracts bodies towards it is called weight.

⇒ Mass. The quantity of matter contained in the body is called its mass.

⇒ Inertial Mass. This mass measures the resistance which is produced due to change in the position of rest to motion.

⇒ Universal Gravitational Constant. It is the force which acts between two bodies each of unit mass and lying unit distance apart.

⇒ Kepler’s first law. All planets move around the sun in elliptical orbits. Kepler’s second law. The line joining planet and sun sweeps out equal area in equal interval of time.

⇒ Kepler’s third law. Cube of mean distance ‘r’ of the planet from the sun is proportional to the square of its orbital period.

Ans.— Newton’s universal law of gravitation. This law states that every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them.

This force always acts along the line joining their centres.

If m₁ and m₂ are the masses of two objects lying distance d apart, then force F between them is :

F = Gm₁ m₂ / d²

where G is a constant, called universal gravitational constant.

Ans.— Let ‘m’ be the mass of object on the earth and the mass of earth be ‘M’. If ‘R’ is the radius of the earth, then the formula for gravitational force between earth and object is :

F = GmM / R²

Since the size of the object is very small as compared to that of the earth, therefore distance between centre of object and centre of the earth is taken to be equal to radius of the earth.

Ans.— Free Fall. An object is said to be in a state of free fall when it falls towards the earth under the influence of gravitational force between the object and the earth. There is no change in the direction of motion of the body but value of velocity keeps changing due to attraction of earth. It falls towards earth with an acceleration of 9.8 m s -².

Ans.— Acceleration due to gravity. The acceleration produced in the motion of a body falling under the force of gravity is called acceleration due to gravity. It is denoted by ‘g’.

Ans.— Difference between mass and weight :

Mass	Weight
Mass of the quantity of matter contained in a body and is the measure of its inertia.	Weight of a body is the force with which a body is attracted towards the centre of the earth.
Mass of a body remains constant at all places.	Weight of a body (W = mg) changes from place to place due to the change in the value of acceleration due to gravity ‘g’.
Mass is a scalar quantity.	Weight is a vector quantity.
Mass is measured by a pan balance.	Weight of a body is measured by a spring balance.
Mass of a body is never zero.	Weight of a body is zero at the centre of the earth.
The unit of mass is kg.	The unit of weight is newton or kg-wt.

Ans.— We know that, Mass of earth (M_e) = 100 × Mass of moon (M_m)

Radius of earth (R_e) = 4 × Radius of moon (R_m)

Since the mass and radius of moon is less than that of the earth therefore, moon exerts

lesser {1/6 th) force of attraction on the object. Hence the weight of the object on moon is 1/6 th of the weight of the same object on earth.

Ans.— Let m₁ and m₂ be the masses of the two objects A and B respectively and ‘r’ be m2 the distance between their centres. Therefore, according to the law of Gravitation, the force of attraction between them is given ahead :

F = Gm₁ x m₂ / r²

If the distance between the two objects be reduced to half, then

∴ Force of gravitation between them will be

Using equation (i))

F = 4 × F

Therefore force of attraction will become four times when the distance between the two objects is reduced to half.

Sol.— Suppose F is the gravitational force that acts on an object of mass ‘m’.

∴ F = G. Mm / r²

and  F = mg

From (i) and (ii)

F = GMm / r² = mg

It is clear that F ∝ m but acceleration due to gravity ‘g’ does not depend upon mass ‘m’. Hence all objects (light or heavy) fall with the same speed when there is no air resistance.

Sol.— Here Mass of the object  (m) =  1 kg

Mass of earth (M) = 6 × 10²⁴ kg

Radius of the earth (R) = 6.4 × 10⁶  m

The magnitude of force of gravitation between object of mass 1 kg and the earth

         = 9.77 N

         = 9.8 N (Approx) Ans.

Ans.— The earth attracts the moon with the same force as the force with which the moon attracts the earth. According to Newton’s third law, these two forces are equal and opposite.

Ans.—According to Newton’s third law, the moon also attracts earth with a force equal to that with which the earth attracts the moon. But the earth is much larger than the moon. So, the acceleration produced in the earth (a ∝ 1/m) is very less and is not noticeable.

Ans.— Force of gravitation, F = G – m₁ m₂ / r²

(i) When mass of one body (m₁ or m₂) is doubled, the force gets doubled.

F = G(2m₁) m₂ / r²

= 2G m₁ m₂ / r²

= 2F

(ii) When distance between the bodies is doubled,

i.e., the force becomes one fourth of the original force.

Ans.— Importance of universal law of gravitation :

(i) The gravitational force between the sun and the earth makes the earth move around the sun with a uniform speed.

(ii) The gravitational force between the earth and the moon makes the moon move around the earth with uniform speed.

(iii) The high and low tides are formed in sea due to the gravitational pull exerted by the sun and the moon on the surface of water.

(iv) It is the gravitational pull of the earth, which holds our atmosphere in place.

(v) The gravitational pull of earth keeps us and other bodies firmly on the ground.

Ans.— Acceleration of free fall. It is the acceleration produced when a body falls under the influence of the force of gravitation of the earth alone. Near the surface of the earth, its value is 9.8 m s ^-2.

Ans.— The gravitational force between the earth and an object is called weight of the object.

Ans.— The value of g at the equator is less than that at the poles. Hence, the few gm of gold at poles will measure less when taken to the equator. Therefore, the friend will not agree with the weight of the gold bought.

Ans.— The sheet of paper will experience a larger air resistance due to its large surface area than that of its ball from.

Increased force of friction will reduce the forward driving force due to gravity. Hence sheet of paper falls slower than one that is crumbled into a ball.

Sol.—  Mass of the object on moon = 10 kg

Mass of the object on the earth = 10 kg

Acceleration due to gravity on the earth (g) = 9.8 m s ^-2

Weight of the object on the earth (W) = m × g

= 10 × 9.8

= 98 N Ans.

Now weight of the object on moon’s surface = 1/6 × weight of the object on earth 6

= 1/6 × 98 N

= 16.3 N Ans.

Sol.— Here, the height of the tower, (h) = 19.6 m

Initial velocity of stone, (u) = 0

Acceleration due to gravity, (g) = + 9.8 m s ^–¹

Final velocity of the stone, (v) = ?

Using equation of motion, v² – u² = 2gh

v² – (0)² = 2 × 9.8 × 19.6

v² = 19.6 × 19.6

v = √19.6 × 19.6

= 19.6 m s ^–¹ Ans.

Sol.— Height of the tower = 100 m

Suppose a stone is allowed to fall from point A at the top of tower and another stone is projected vertically upward from point C. These two stones meet at point B after ‘t’ seconds.

Distance covered by first stone (AB) = x

∴ Distance covered by second stone (CB) = (100 – x)

i.e the first stone will cover a distance of 80 m in the downward direction. and second stone will cover upward distance = 100 – x

= 100 – 80

= 20 m Ans.

Ans.— Newton’s universal law of gravitation— Every particle in this universe attracts each and every particle, the force of attraction is

(i) directly proportional to the product of both the masses and.

(ii) Inversely proportional of the square of the distance between the two. This force always acts along the line joining the two masses.

Derivation of Mathematical Formula. From the fig. let there are two balls A and B having masses m₁ and m₂ distance between them is ‘r’.

According to Newton’s third law of motion ball A exerts a force FR_BA on the ball B and ball B exerts a force F_AB on the ball A. These forces are equal and opposite

F_AB = – F_BA

Let, F_AB = – F_BA

then according to law of gravitation

F ∝ m₁m₂      ….(i)

and F ∝ 1/r² ….(ii)

from (i) and (ii)

F ∝ m₁ × m₂  / r²

or, F = G m₁ × m₂  / r²

Where G is universal gravitational constant. This is named so since its numerical value remains constant in whole of the universe and the formula is known as Newton’s universal law of gravitation.

Value of G

G = 6.67 × 10 10^–11 Nm² / kg²

Ans.— By the 16th centuary, a lot of data on the motion of planets had been collected by many astronomers. Johannes Kepler derived three laws based on these data. These are known as Kepler’s laws. These are—

1. Law of orbits (First laws)—The orbit of a planet is an ellipse and the sun is at one of the foci, as shown in fig. In this fig. Sun is shown at O.

2. Law of area (Second laws)— The line joining the planet and sun sweep equal areas in equal intervals of time. Thus, time taken for the motion from A to B is same as for the motion from C to D and area – OAB and OCD are equal.

3. Law of time period (Third law)— The cube of mean distance of a planet from the sun is directly proportional to square of its orbital time period

T² ∝ r³

But Kepler could not give a theory which explained the motion of planets.

Newton showed that due to motion of planets sun exerts force of gravtation on them. i.e.

r³ / T² = constant.

Ans.—  Boyle’s Experiment. As shown in fig. Robert Boyle took a long glass tube. A heavy coin and a piece of paper were placed inside the tube. The ends of the tube were closed. Air from the tube was removed with the help of a vacuum pump. When the tube was quickly inverted it was seen that coin and a piece of paper hit the bottom of the tube at the same time. Now the experiment was repeated with air inside the glass tube.

This time it was observed that a piece of paper falls slowly whereas the coin immediately hit the bottom of glass tube. This experiment proves that in vacuum all bodies irrespective of their masses (both light and heavy) fall towards earth with same acceleration

Ans.— (a) Consider a body of mass ‘m’ lying on the surface of earth. Suppose M are respectively mass and radius of earth.

Let F be the force of gravity acting on the body

This acceleration is called acceleration due to gravity

∴ g = Gm / R²

This equation is free from mass ‘m’ . This shows that due to force of gravity the acceleration produced in an object is independent of its mass.

Ans.— Variation in the value of acceleration due to following factors : Variation in g with altitude-Value of ‘g’ is maximum on the surface of earth. As we move in upward direction (higher altitudes) value of ‘g’ goes on decreasing. We can calculate value of ‘g’ at altitude using a mathematical formula. If

g_e = acceleration due to gravity on the surface of earth

g_h = acceleration due to gravity at height h

R = radius of earth

we know

Earth is not exactly spherical. It is some what egg shaped. Its radius at than that at equator as shown in fig.

As shown in fig. radius of earth at equator is 6378 km and radius of earth at poles is 6357 km. Thus, value of g_p at poles is g_p = 9.831m s ^–² (maximum) and minimum value at equator is g = 9.782 m s^-2. We use average value of g calculated from g_e and g_{p .}

(iii) Effect of depth— If we go deep under the earth e.g. in caves or in mines, value of ‘g’ is decreased value of g goes on decreasing, if depth goes on increasing. At the centre of earth, value of g is zero.

W_d / W_e = gd / g_e = [1 – d/R]

                                           Or

Ans.— Relation between ‘g’ and ‘G’. Suppose the earth is a sphere of mass M and radius R, Consider a body of mass m lying at a distance ‘r’ from the centre of the earth. According to Newton’s law of gravitation, the force of attraction between the earth and the body,

F = GMm / r²  …(i)

This force of gravity produces an acceleration ‘g’, is the body of mass m.

Hence, from Newton’s second law,

F = Mass × Acceleration

F = m × g ….(ii)

From equations (i) and (ii) we get

mg =  GMm /  r²

or,  g = GM / r² ….(iii)

This equation gives relation between acceleration due to gravity ‘g’ at points far away from the earth and gravitational constant ‘G’.

Since (iii) does not involve ‘m’ it is therefore evident that ‘g’ does not depend upon the mass of the body.

Ans.—  According to Newton’s law of Gravitation there exists of mutual force of attraction between two objects. Therefore, neither the earth applies force on iron nor iron on earth. Since the mass of iron is less than the mass of the earth, therefore earth attracts 1 kg mass towards it with a greater force which is noticeable.

Ans.— G is called universal gravitational constant because its numerical value is same in the whole universe. This value is G = 6.67 x 10^-11 Nm²/ kg².

Ans. From the relation between the acceleration due to gravity ‘g’ and universal gravitational constant G, we know

g = GM / r²

From this From this equation it is evident that the value of ‘g’ does not depend upon the mass of the body. Thus we reach a conclusion that at a given place the value of g is same for different bodies.

Ans.—  We know value of g goes on decreasing as we continue moving deep into the earth and value of acceleration due to gravity (g) = 0 at the centre of earth. Thus, a body whose mass is m,

Weight of body = m × 0 = 0

Therefore, body becomes weightless.

Ans.— Value of g decreases with altitude, thus gravitational force acting on ball at hills is less as a result ball jumps higher at hills than at planes.

Ans.—  We know that value of ‘g’ on the surface of earth is 9.8 m/s² and the relation for weight of an object is :

w = m × g

9.8 = m × 9.8

or, m = 9.8 / 9.8

∴ m = 1 kg

The given statement therefore means the mass of the object on earth is 1 kg.

Ans.—A body falling freely under gravity executes uniform accelerated motion. If bodies with different masses and different shapes are allowed to fall freely in vacuum, they all will have same acceleration due to gravity.

Ans.—  Difference between g and G :

Acceteration due to gravity (g)	Gravitational constant (G).
It represents acceleration acquired by the body due to on insiero fois gravity.	It represents force of attraction between two masses of 1 kg each lying 1 m apart.
Its value is different at different places on earth surface.	Its value is constant at all places. Thus, it is called universal constant.
Its value at the surface of earth 900 is 9.8 m/s².	Its value is 9.67 x 10-11 Nm²kg-².
It is a vector quantity.	It is a scalar quantity.

Ans.— The value of ‘g’ at Antarctica is not same as on equator. The value of ‘g’ increases on Antarctica therefore, sugar bought at any place on equitorial line when taken to Antarctica would have more weight but its mass will remain the same because mass is a constant quantity.

Ans.— When we move our finger, then distance between finger and all other things in the universe change and as a result force of gravitation also changes. Thus, all the things get disturbed, although this disturbance is negligible.

Ans.— Gravitation. Gravitation is the force of attraction between any two bodies in the universe. The attraction between the sun and the earth, the attraction between a table and a chair are examples of gravitation.

Gravity. Gravity is a special case of gravitation when one of the two bodies is the earth. Gravity is the attraction between the earth and any object lying on or near its surface. A ball thrown upward falls back on the surface of the earth due to earth’s force of gravity.

Ans.— Because of very small value of G, the force of attraction between any two such ordinary sized bodies is so small that it cannot produce motion in them.

Ans.— The apple also attracts the earth with an equal and opposite force. The mass of the earth is very large compared to that of apple. So, the acceleration produced in earth is very small as compared to that in the apple. Hence, the motion of the earth towards the apple is not appreciable and therefore, is not noticeable.

Ans.—  In the absence of force of gravity, the centripetal force required to keep us rotating along the earth would not be available. As a result would fly off along the tangent to with into the space.

Distance between two spheres, (r) = 3 m

Gravitational constant (G) = 6.67 × 10^-11  Nm²  / kg²

We know, F = G. m₁ × m₂  / r²

F = 6.67 × 10^-11 × 1 × 1 / (3)²

Ans.—  Nearly 1/6 th of its value on earth.

Ans.— It is Nm² kg -².

Ans.—  It is about 6 × 10²⁴   kg.

Ans.— Mass is the basic and essential property. It is constant everywhere. Weight of a body varies from place to place.

Ans.— It is newton (N).

Ans.— Same i.e., 5 m s^-2  since g at a place is independent of mass of the body.

Ans.—The g at moon surface is nearly 1/6th of that at the surface of earth. Hence can jump six times higher on the moon with a given initial velocity.

Ans.— (G) = 6.67 x 10^-11 Nm²/kg²

The value of gravitational constant.

Ans.— Since G is universal constant so its value on moon surface will be same as on the earth surface i.e. G = 6.67 × 110^-11 Nm²/kg².

Ans.— The gravitational force between two objects depends on : (i) their masses (ii) distance between them.

Ans.—  F = G Mm / r²

Ans.—No, mass of body can never be zero.

Ans.— The weight of an object on the moon is 1/6th its weight on the earth.

Ans.— Mass is a constant quantity. So, it can not be more or less than 42 kg.

Ans.—The value of ‘g’ increases as we move from equator to poles.

Ans.—  Weight of the object on earth

(W) = m × g

= 10 kg × 10 m s -²

= 100 N

Ans.— Nm²/kg².