Gravitation

Question (1) How does the force of gravitation between two objects change when the distance between them is reduced to half?

Answer

According to Inverse Square rule, the force of gravitation is indirectly proportional to the square of distance between objects.

This means `F prop 1/d^2` -------- (i)

Where, F is the force of gravitation and d is the distance between object.

Now, let the distance becomes half

That is distance = `d/2`

Now, let force of gravitation = F₁ in the case of half distance.

Thus, according to Inverse Square Rule,

`F_1 prop 1/(d//2)^2`

`=>F_1 prop 1/(d^2//4)`

`=>F_1 prop 4/d^2` ------------- (ii)

Now, `F/F_1 = (1//d^2)/(4//d^2)`

`=>F/F_1 = 1/d^2\ xx d^2/4`

`=>F/F_1 = 1/4`

That is F : F₁ = 1:4

Thus, the force of gravitation becomes four times greater when distance between objects is reduced to half.

Question (2) Gravitational Force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?

Answer

We know that

Force = mass × acceleration due to gravity.

The acceleration due to gravity, `g=GM/d^2`

Where,

G = Gravitational constant

M = Mass of earth

d = distance of object from earth

g = acceleration due to gravity

Here it is clear that the acceleration due to gravity does not depend upon the mass of the object. Therefore, all objects whether heavier or lighter falls on the earth with same rate of acceleration.

Question (3) What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is 6 ×10²⁴ kg and radius of the earth is 6.4 ×10⁶ m.)

Answer

Given,

Mass of ball, m = 1kg

Mass of earth, M = 6 × 10²⁴ kg

Radius of earth = 6.4 × 10⁶ m

G = 6.67 × 10^–11

Here, as the radius of ball is very small compare to that of the radius of earth, hence, it is considered as negligible. Hence, the radius of earth is considered the distance between the centre of ball and the centre of earth.

Therefore, the distance between the centres of earth and ball = 6.4 × 10⁶ m

Now, we know that, `F=G(Mxxm)/d^2`

`=>F=6.67xx10^(-11)xx(6xx10^(24)xx1)/(6.4xx10^6)^2\ N`

`=>F=6.67xx10^(-11)xx(6xx10^(24)xx1)/(6.4xx6.4xx10^12)\ N`

`=>F=(6.67xx6xx10^24)/(6.4xx6.4xx10^23)\ N`

`=>F=9.8144\ N`

`=>F~~9.8\ N`

Thus, Gravitation force between given object and earth is equal to 9.8 N

Question (4) The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?

Answer

The earth and moon attracts each other with the same magnitude of force of attraction, because according to Newton's Third Law of Motion there is reaction for every action. And the magnitude of force of action and reaction are always equal but in opposite direction.

Question (5) If the moon attracts the earth, why does the earth not move towards the moon?

Answer

We know that Force, F = Mass, m × Acceleration, a

`=>a=F/m`

This means acceleration produced by a body is inversely proportional to the mass of the object.

In the case of earth, acceleration produced because of the force of attraction of moon on the earth, is very small because of huge mass of earth.

Therefore, we cannot observe the movement of earth towards the moon.

Question (6) What happens to the force between two objects, if

(i) the mass of one object is doubled?

(ii) the distance between the objects is doubled and tripled?

(iii) the masses of both objects are doubled?

Answer

(i) According to the Universal Law of Gravitation, force of attraction between two objects is directly proportional to the produce of their masses.

This means `F prop M xx m`

Here since Force of attraction between two objects is directly proportional to the mass of object, thus if mass of one object is doubled then force of attraction will also be doubled.

(ii) According to the Universal Law of Gravitation the force of attraction between object is indirectly proportional to the square of distance between object.

This means, `F\ prop\ 1/d^2`

Hence,

(a) If the distance between object is doubled,

This means distance between objects, d will become 2d.

Therefore, `F prop 1/(4d^2)`

Therefore, the force of attraction between objects will become `1/4th` i.e. decreased by 4 times.

(b) If the distance between object is tripled,

This means distance between objects, d will become 3d

Therefore, `F prop 1/(9d^2)`

Therefore, the force of attraction between objects will become `1/9th`, i.e. decreased by 9 times.

(iii) When mass of both objects are doubled,

Therefore, `F prop 2\ Mxx2\ m`

`=>F prop 4Mxxm`

This means the force will be increased by 4 times.

Question (7) What is the importance of universal law of gravitation?

Answer

Importance of Universal Law of Gravitation:

After giving the Universal Law of Gravitation, Newton explained satisfactorily many natural phenomenon, such as

(a) Cause of falling of all objects on the ground

(b) Cause of neap and tide in the ocean

(c) Motion of planets round the sun

(d) Motion of moon around the earth

(e) The force that bind us and other objects to the earth

Question (8) What is the acceleration of free fall?

Answer

When an object falls towards earth; its velocity changes with a constant rate of acceleration. The rate of change of acceleration does not depend upon the mass of the object.

It is calculated the rate change of acceleration is 9.8 m s^–2 of a free falling object. This means the velocity of the free falling object increased at the rate of 9.8 m^–2. The acceleration produced because of the gravitation of earth in a free falling object is called acceleration of free fall due to gravity.

Hence, acceleration of free fall is 9.8 m s^–2.

Question (9) What do we call the gravitational force between the earth and an object?

Answer

The gravitational force between the earth and on object is called the gravity of earth or gravitational force of earth.

Question (10) Amit buys few grams of gold at the poles as per the instruction of one of his friends. He hands over the same when he meets him at the equator. Will the friend agree with the weight of gold bought? If not, why? [Hint: The value of `g` is greater at the poles than at the equator.]

Answer

Amit's friend does not agree with the weight of the gold because,

Mass of an object is constant everywhere but weight depends upon the value of `g`.

And we know that the weight (W) of an object is equal to the product of mass (m) and value of `g`.

This means `W=mxxg`

And since the value of `g` is greater at the pole than at the equator; thus the weight of the gold becomes less at equator compare to pole.

Hence, a weighing machine weighs the same quantity of gold less at the equator.

Question (11) Why does a sheet of paper fall slower than one that is crumpled into a ball?

Answer

The buoyant force increases with the increase in area. The area sheet of paper is more than the area of the same sheet when crumpled.

Therefore, a sheet of paper falls slower than one that is crumpled into ball. This happens because a sheet of paper experience more buoyant force or air resistance than a one that is crumpled into a ball.