Solution of Gravitation (Page No - 102) - Physics by Lakhmir Singh, Class 9 | Extra Documents & Tests for Class 9 PDF Download

Question 45:
A force of 20 N acts upon a body whose weight is 9.8 N. What is the mass of the body and how much is its acceleration ? (g = 9.8 m s^-2).
Solution :
Weight= 9.8N
W= m x g
9.8 =m x 9.8
m= 1kg
Force, F= mass x acceleration
20 N = 1kg x a
Acceleration,
a=20m/s²

Question 46:
A stone resting on the ground has a gravitational force of 20 N acting on it. What is the weight of the stone ? What is its mass ? (g = 10 m/s²).
Solution :
Weight of the stone = Gravitational force acting on it = 20 N
Weight, W= m x g
20=m x 10
m=2 kg

Question 47:
An object has mass of 20 kg on earth. What will be its (i) mass, and (ii) weight, on the moon ? (g on moon = 1.6 m/s²).
Solution :
(i) Its mass will be 20 kg as mass is a constant quantity.
(ii)Weight, W= m x g =20 x 1.6=32N

Question 48:
Which is more fundamental, the mass of a body or its weight ? Why ?
Solution :
The mass of a body is more fundamental because mass of a body is constant and does not change from place to place.

Question 49:
How much is the weight of an object on the moon as compared to its weight on the earth ? Give reason for your answer

Solution :
The weight of an object on the moon is about one-sixth of its weight on the earth. This is because the value of acceleration due to gravity on the moon is about
one-sixth of that on the earth.

Question 50:
(a) Define mass of a body. What is the SI unit of mass ?
(b) Define weight of a body. What is the SI unit of weight ?
(c) What is the relation between mass and weight of a body ?
Solution :
(a) The mass of a body is the quantity of matter contained in it. The SI unit of mass is kilogram (kg).
(b) The weight of a body is the force with which it is attracted towards the centre of the earth. The SI unit of weight is newton (N).
(c) Weight, W =m x g, i.e. the weight of a body is directly proportional to its mass.

Question 51:
(a) State the universal law of gravitation. Name the scientist who gave this law.
(b) Define gravitational constant. What are the units of gravitational constant ?
Solution :
(a) According to universal law of gravitation: Every body in the universe attracts every other body with a force (F) which is directly proportional to the product of their masses (m and M) and inversely proportional to the square of the distance (d) between them.

(b) The gravitational constant G is numerically equal to the force of gravitation which exists between two bodies of unit masses kept at a unit distance from each other. 

Sir Isaac Newton gave this law. 

Question 52:
(a) What do you understand by the term ‘acceleration due to gravity of earth’ ?
(b) What is the usual value of the acceleration due to gravity of earth ?
(c) State the SI unit of acceleration due to gravity.
Solution :
(a) The uniform acceleration produced in a freely falling body due to the gravitational force of the earth is called acceleration due to gravity of earth.
(b) Usual value of acceleration due to gravity, g=9.8 m/s².
(c) SI unit of acceleration due to gravity is m/s².

Question 53:
(a) Is the acceleration due to gravity of earth ‘g’ a constant ? Discuss.
(b) Calculate the acceleration due to gravity on the surface of a satellite having a mass of 7.4 x 10²² kg and a radius of 1.74 x 10⁶ m (G = 6.7 x 10^-11 Nm²/kg²). Which satellite do you think it could be ?
Solution :
(a) No, the value of acceleration due to gravity (g) is not constant at all the places on the surface of the earth. Since the radius of the earth is minimum at the poles and maximum at the equator, the value of g is maximum at the poles and minimum at the equator. As we go up from the surface of the earth, the distance from the centre of the earth increases and hence the value of g decreases. The value of g also decreases as we go down inside the earth.

As the value of g = 1.637m/s² , which is one sixth of the value of g on earth, the satellite could be moon.

Question 54:
State and explain Kepler’s laws of planetary motion. Draw diagrams to illustrate these laws.
Solution :
Kepler’s first law: The planets move in elliptical orbits around the sun, with the sun at one of the two foci of the elliptical orbit. This law means that the orbit of a planet around the sun is an ellipse and not an exact circle. An elliptical path has two foci, and the sun is at one of the two foci of the elliptical path.
Kepler’s Second law states that: Each planet revolves around the sun in such a way that the line joining the planet to the sun sweeps over equal areas in equal intervals of time. This means that a planet does not move with constant speed around the sun. The speed is greater when the planet is nearer the sun, and less when the planet is farther away from the sun.
Kepler’s Third Law states that: The cube of the mean distance of a planet from the sun is directly proportional to the square of time it takes to move around the sun. 

Kepler's first law : the planet move in elliptical orbits around the sun, with the sun at one of the two foci of elliptical orbit. This law means that the orbit of a planet around the sun is an ellipse and not an exact circle. An elliptical path has two foci, and the sun is at one of the two foci of the elliptical path.

Kepler's second law state that : Each planet revolve around the sun in such a way that the line joining the planet to the sun sweeps over equal areas in equal intervals of time. This mean that a planet does not move with constant speed around the sun. The speed is greater when the planet nearer the sun, and less when the planet is farther away from the sun.

Kepler's third law sate that : The cube of the mean distance of planet from the sun is directly proportional to the square of time it takes to move around the sun.

Question 55:
The mass of a planet is 6 x 10²⁴ kg and its diameter is 12.8 x 10³ If the value of gravitational constant be 6.7 x 10^-11 Nm²/kg², calculate the value of acceleration due to gravity on the surface of the planet. What planet could this be ?
Solution :
Acceleration due to gravity, 

As the value of g = 9.8m/s², the planet could be earth.