GRAVITATION

Q1] What are the effect of a force acting on an object?

Ans) The effects of a force acting on an object are as follow:
a) Speed can change
b) Direction can change
c) Speed and direction both can be change
d) Shape can change
Q2] What types of forces are you familiar with?
Ans) Gravitational force, Frictional force, Magnetic force and Mechanical force
Q3] What do you know about the gravitation force?
Ans) gravitation force is the force exerted by the earth which pulls object
towards itself in perpendicular directional

 Newton’s laws of motion

i. A body continues to be in a state of rest or of uniform motion unless it is
acted upon by an external unbalance force.
ii. The rate of change of momentum is directly proportional to the applied
force and it acts in the direction of the applied force.
iii.To every action there is an equal and oppostite reaction.
Q1] Definition of centripetal force?
Ans) A force acts on any object moving along a circle and it is directed towards
the centre of the circle.this is called centripetal force.
Q2] Definition of ellipse.
An ellipse is the curve obtained when a cone is cut by an inclined plane. It has
two focal points. The sum of the distances to the two focal points from every
points on the curve is constant, F1 and F2 are two focal points of the ellipse
shown in figure if A,B and C are three points on the ellipse then, AF 1 + AF2 = BF1
= CF1 + CF2
 GRAVITATION

Q3] Kepler’s Laws:

Kepler’s first law:
The orbit of a planet is an ellipse with the sun at one of the foci’
The following figure shows the elliptical orbit of a planet revolving
around the sun the position of the sun is indicated by 5.
Kepler’s second law:
The line joining the planet & the sun sweeps equal areas in equal intervals of
time’
AB & CD distances covered by the planet in equal time i.e after equal
intervals of time, the position of the planet starting from A & C are
shown by B & D respectively.
The straight lines AS & CS sweeps equal areas in equal intervals of time
i.e areas ASB & CSD are equal.

Kepler’s third law:

‘The square of its period of revolution around the sun is directly proportional
to the cube of the mean distance of a plant from the sun’
Thus, if r is the average distance of the planet from the sun & T is its
period of revolution then;
2
2 3 T
T a r i.e 3 ¿ constant ¿ K →(1)
r
 GRAVITATION

State newton’s universal law of gravitation


→ Every object in the universe attracts every other object with a definite

force. This force is directly proportional to the product of the masses of the

two objects and is inversely proportional to the square of the distance

between them.

Two objects with masses m and m kept at a distance d from each other.
 1 2
mathematically, the gravitational force of attraction between these two

bodies can be written as:

m 1 m2 Gm1 m 2
 F× D2 or F= D
2

here, G is the constant of proportionality and is called the universal

gravitational constant.
 The value of G is the gravitational force acting between two Unit
masses kept at a unit distance away from each other. Thus, in S1 units,
the value of G is equal to the gravitational force between two masses of
1kg 1m apart.
 GRAVITATION

 Value of g on the surface of the earth:

Consider a body having m on the surface of the earth consider a body
having m on the surface of the earth.
F= GM m where G is = universal constant of gravitation
R2

M= mass of the earth

R= radius of earth
Let g be the acceleration due to gravity
The body experiences a force
F= mg (ii) due to acceleration due to gravity
From eqn (i) and (ii)
GMm
mg= 2
R
GM
∴ g= 2
R

= 9.832 m/s2

Q Differentiate between mass and weight

mass Weight
i. Mass is the amount of matter i. Weight is the force with
present in a object which the earth attracts the
object

ii. Mass is a scalar quantity ii. Weight is vector quantity

iii. The S1 unit of mass is kg iii. The S1 unit of weight
 GRAVITATION
newton
iv. The value of mass remains iv. The value of weight
constant everywhere changes from place to place
depending on g

Q1] Answer the following question

1. Will the mass and weight of an object on the earth be same as
their values on mars? Why?
Ans) the mass will remain the same but the weight will change
because of the difference in the value of acceleration due to gravity.
2. What is free fall?
Ans) Whenever an object moves under the influence of the force of
gravity alone, it is said to be falling freely. In free fall, the initial
velocity of the object is zero and goes on increasing due to the
acceleration due to gravity of the earth.
3. What is acceleration due to gravity?
Ans] The gravitation force due to the earth on a body result in its
acceleration. This is called acceleration due to gravity and is donated
by (g)
4. Escape velocity.
Ans] When on object is thrown upwards with such an initial velocity
that it is able to overcome the downward pull by the earth and can
escape the earth forever and will not fall back at the earth, this
velocity is called escape velocity.
5. If the value of g suddenly becomes twice its value, it will become
two times more difficult to pull a heavy object along the floor. Why?
Ans] When an object is pulled along a floor, there is frictional force to
be overcome. If the value of g increases, the force due to acceleration
due to gravity (F= mg) also increases. As a result, it becomes difficult
to pull a heavy object along the floor.
6. Explain why the value of g is zero at the centre of the earth?
GM
Ans] g= 2 . The value of g changes as we go inside the earth. R is the
R
radius of the earth and as we go inside the earth, the value of R
decreases. At the same time the part of the earth which contributes
 GRAVITATION
towards the gravitation force also decreases. Hence the value of g
goes on decreasing. At the centre of the earth R becomes zero and
hence the value of g becomes zero.

Q2] give reasons:

1. The moon and the artificial satellite that orbit the earth do not fall
on the earth?
Ans) The gravitation force due to the earth acts on the moon
because of which it revolves around the earth. The earth attracts
them towards itself but they do not fall on the earth. This is
because of the velocity of the moon and the satellites along their
orbits. If this velocity was not there, they would have fallen on the
earth.
2. How does the value of g changes along surface of the earth?
Ans) The reason is that the shape of earth is not exactly spherical
and so the distance of a point on the surface of the earth from its
centre differs somewhat from place to place. Due to its rotation,
the earth bulges at the equator and is flatter at the poles. Its
radius is largest at the equator and smaller at the poles. The value
of g is thus highest (9.832 m\s) at the poles and deceases slowly
with decreasing latitude. it is lowest (9.78 m\s2) at the equator.
3. How does the values of g change with height?
Ans) As we go above the earth’s surface, the value of r increases
and the value of g decreases. This decrease is rather small for
heights which are small in comparison to the earth’s radius. The
change in the value of g due to it is negligible. On the other hand,
when we consider an artificial satellite orbiting the earth, we have
to take into account the change in the value of g due to the large
change in the distance of the satellite from the centre of the
earth.