CIRCULAR MOTION AND GRAVITATION
IMPORTANT QUESTIONS OF PAST PAPERS:
1. Define centripetal force and what are the factors depends on which it depends? Write down the formula of centripetal force. (2009)2. State Newton law of gravitation derives the formula of mass of earth with its help. (2013)
3.States Newton’s law of gravitation and prove that F= G m1m2/r2 . (2009, 2013)
4. Define orbital velocity and derive the formula V= √ g Re. (2016)
IMPORTANT SYMBOLS:
• Centripetal Force = Fc• Centripetal acceleration = ac
• Mass of Earth = Me
• Gravitation constant = G
• Centripetal acceleration = ac
• Orbital velocity = V
• Distance & radius = r
• gravity = g
IMPORTANT FORMULA’S:
Questions/ Answer
Q. 1: Define the following terms with formulas and unit.i.Circular motion
ii. Centripetal force
iii. Centripetal acceleration
iv. Centrifugal force
Ans:
i. CIRCULAR MOTION: When an object revolves in a circular orbit its motion is said to be Circular Motion.
OR
The force which acts towards the center along the radius of a circular path on which the body is moving with a uniform velocity is called Centripetal Force.ii. CENTRIPETAL FORCE: The force which is responsible for the motion of a body in circular orbit is called Centripetal Force.
Formula:
Unit: unit of Centripetal Force is Newton N.
iii. CENTRIPETAL ACCELERATION: The change of the velocity on the circumference of the circle is called Centripetal Acceleration.
Formula:
Unit: Unit of Centripetal Acceleration is msec-2 or m/sec2
iv. CENTRIFUGAL FORCE: The force which is directed away from the centre of circle is called Centrifugal Force. It is an opposite and equal reaction of centripetal force.
OR
The force which is reaction of the Centripetal Force is called centrifugal force.
Formula:
Unit: Unit of Centripetal Acceleration is msec-2 or m/sec2
Q.2: What are the factors which depend on centripetal force?
Ans: There are three factors are as follow,
i. The mass of the Object increases.
ii. The speed of the Object increases.
iii. The radius of the circle in which it is travelling decreases.
Q.3: Show that Mathematically
.Ans: CENTRIPETAL FORCE: The force which is responsible for the motion of a body in circular orbit is called Centripetal Force.
MATHEMATICAL EXPRESSION:
If a body of mass m is moving in a circular path the magnitude of centripetal force Fc is given by the equation
Fc = mac
ac is the centripetal acceleration, if r is the radius of the circle and V is the velocity then magnitude of centripetal acceleration is given by
Putting the value of ac
Q. 4: States Newton’s law of gravitation and prove that F= G π¦π π¦π / π«π
Ans: NEWTON LAW OF GRAVITATION:
“Everybody in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square root of the distance between their centers”.
MATHEMATICALLY:
Consider two spherical bodies A and B having the masses π¦π and π¦π respectively. The distance between their centers is r.
Q.5: State Newton’s law of gravitation derives the formula of mass of earth with its help.
Ans:NEWTON’S LAW OF GRAVITATION:
The mass of earth can be determined with the help of Newton’s law of gravitation.
Consider a body of mass “m” placed on the surface of earth. If “Me” be the mass of the earth and “Re” its radius than the force with which the earth attracts the body towards its center is given by equation:
Q.6: Explain how the value of “g” decreases with a change in the altitude.
Ans: VARIATION OF “g” ALTITUDE: Consider a body of mass “m” on the surface of the earth, the gravitational force of attraction between the body and earth is equal to the m weight of the body.
Since “G” and “Me” are constant the acceleration due to gravity “g” decreases increasing distances R from the center of the earth. Therefore,
Q.7: Define orbital velocity and derive the formula V= √gRe.
Ans:ORBITAL VELOCITY: The velocity of an artificial satellite or a natural satellite which moves round the earth at a specific height is called orbital velocity.
MATHEMATICALLY:
Let a satellite having mass “m” be moving in an orbit of radius with velocity “V”. the gravitational force of attraction between the satellite and the earth provides the necessary centripetal force of the satellite.
Combining equation (i) and (ii)
V2 = gR
If the satellite is revolving close to the surface of the earth then,
V= √gRe
From above formula, the orbital velocity has been calculated as,
V= 7290 Kms-2
Q.8: What is satellite? What are natural and artificial satellites?
Ans:SATELLITE: An object revolve around a planet in a fixed orbit is called satellite.
➤ NATURAL SATELLITE: Satellite which naturally exists in the universe and are revolving around a planet is called as Natural Satellite.
For example moon.
➤ ARTIFICIAL SATELLITE: The Satellite sent by the Scientists which moves round the earth are called Artificial Satellite.
For example telecommunication and space research etc.
Q.9: What is banking of road? What are advantages of it?
Ans: BANKING OF ROAD: The outer edge of the curved roads is made higher than inner edges. This is called banking of road.
ADVANTAGES OF BANKING ROAD: When the vehicle exceeds a certain limits, turning a corner the centripetal force is unable to keep the vehicle moving in a circle and the vehicle tends to skit away from the center. The banker road keeps the vehicle moving safely around the curve. The speed limits are mentioned around the curves on the roads for safe driving.
Q.10: Write down the difference between “G” and “g”.
Ans:
| G | g |
|---|---|
| • It represents gravitational constant. | • It represents acceleration due to gravity. |
| • It is a scalar quantity. | • It is a vector quantity. |
| • It remains constant. | • It varies place to place. |
| • Its value 6.67×10-11 Nm2/kg2. | • Its value 9.8 m/sec2. |
Prepared By: Sir Waseem
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