Question on Class IX » Science » Gravitation » The Universal Law Of Gravitation.

Q.1. When we move from the poles to the equator. Hence, the value of ‘ g ’ decreases. Why

Ans: The shape of earth is an ellipse so when we move from the poles to the equator the radius of the earth R increases. Hence, the value of ‘ g ’ decreases because value 'g' is inversely proportional to the radius of earth. g = GM/R^{2}

Q. 2. What is the diffrence between centrifugal force and centripetal force?

Ans: Centripetal Force

(i) It is the force that keeps a body in circular path.
(ii) It acts toward the center.

Centrifugal Force

(i) It is the pseudo force that tries to make a body fly off the circular path.
(ii) It acts outward the center.

Q.3. Explain :Centrifugal force and Centripetal force?

Ans: A force which is required to move a body uniformly in a circle is known as centripetal force. This force acts along the radius and towards the center of the circle,

Centrifugal force arises when a body is moving actually along a circular path, by virtue of tendency of the body to regain its natural straight line path. This force acts along the radius and away from the center of the circle.

Q.4 an astronaut has 80 kg mass on earth (a)what is his weight on earth? (b) what will be his mass and weight on mars where g=3.7 m/s^{2}

Ans: Mass of astronaut = 80 kg

Weight on earth = mg = (80)(9.8) N = 784 N Weight on mars = mg' = (80)(3.7) N = 296 N

Q.5. A certain particle has a weight of 30N at a place where the acceleration due to gravity is 9.8 m/s^{2}

(a) What are its mass and weight at a place where acceleration due to gravity is 3.5 m/s square

(b) What are its mass and weight at a place where acceleration due to gravity is 0

Ans (a) Weight of the body, W = 30 N =mg Mass of the body, m = W/g =30 /9.8= 3.06 kg

New weight of the body, W' = mg' = (3.06) (3.5) N = 10.71 N

(b) . Mass remains the same but weight becomes zero.

Q.6. Derive the inverse square of Newton.

Ans:Keller’s Third Law can be written as

T2 = kr3

or T2 = (4π2/GM).r3 ..............(1)

now, we know that the time period, T = 2πr/v,

so (1) becomes (2πr/v)2 = (4π2/GM).r3

or 4π2 (r/v)2 = (4π2/GM).r3

or (r/v)2 = (1/GM).r3 = r3/GM .......................(2)

we know that, centripetal acceleration a = v2/r [from ma = mv2/r] thus, equation (2) becomes

r/a = r3/GM

or 1/a = r2/GM

or a = GM/r2 .......................... (3)

and we also know that F = ma, thus using equation (3) we would get

F = ma = m(GM/r2)

thus, we have derived the Newton's Law of Gravitation, which is

F = GMm/r 2 from Kepler's Third Law

Q,7. What is the difference between gravity and gravitation?

Ans: Gravity is defined as the ability of earth to attract another body by virtue of their masses.
Gravitation is the phenomenon which explains the force of attraction between two masses separated by a certain distance. This force is known as Gravitational Force

Q.8.What are these :(( i) Product Rule (ii) Inverse Square rule (iii) Universal gravitational constant iv) Universal law of gravitation:

Ans: (i) Product rule: Force between two mass separated by a distance is directly proportional to the product of the two masses.

(ii) Inverse square law means that the force is inversely proportional to the square of the distance between two objects. Gravitational force is an example of inverse square law. The relation between the force of gravitation and distance is F∝1/r2

(iii)Universal gravitational constant: The constant of proportionality is called the universal gravitational constant. Gravitational constant is defined as the force of attraction between two unit masses kept at unit distance. For example if we choose m 1, m 2 such that, m 1 = m 2 = 1 and keep them at a unit distance (r =1), gravitational constant is equal to gravitation force of attraction between them

(iv) Universal law of gravitation: a force of attraction between two masses separated by some distance. The gravitational force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

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