Solved Examples
Q.1.
What is the force of gravity acting on an object of mass 2000 kg at the Earth’s surface?
Given:
Mass of Earth (m1) = 5.98 × 1024kg
Mass of object (m2) = 2000kg
The radius of the Earth (r)= 6.38 × 106m
Acceleration due to gravity (g) = 9.8 m/s2
Universal constant (G) = 6.67 x 10-11 N m2 / kg2
Solution:
F = Gm1m2/r2
F = ( 6.67 x 10-11) (5.98 × 1024)(2 x 103)/(6.38 × 106)2
F = (7.978 x 1017)/ (4.07044 × 1013)
F = 1.959 x 104 or F = 19.59 N
Q.2.
What is the force of gravity acting on an object of mass 1000 kg at 20,000 meters above the Earth’s surface?
Given:
Mass of Earth (m1) = 5.98 × 1024kg
Mass of object (m2) = 1000kg
The radius of the Earth (r)= 6.38 × 106m
Acceleration due to gravity (g) = 9.8 m/s2
Universal constant (G) = 6.67 x 10-11 N m2 / kg2
h = 2 x 104 m
Solution:
F = Gm1m2/(r +h)2
F = ( 6.67 x 10-11) (5.98 × 1024)(1 x 103)/(6.38 × 106 + 2 x 104 )2
F = (3.988 x 1017)/(4.058 x 1013)
F = 9,827.50
F = 0.9827 x 104
Q.3 :
Find the gravitational force of attraction between two elephants, one of mass 1000 kg and the other of mass 800 kg, if the distance between them is 5 m.
Solution:
Given: m1 = 1000 kg, m2 = 800 kg, r = 5 m
The formula for gravitational force is given as:
F = Gm1m2/r2
Here, G = 6.67 ×10−11N⋅ m2/kg2
Substituting the values in the formula, we have:
F = 6.67×10−11N⋅m2/kg2)(1000kg)(800kg)/52
F = 2.1 × 10-6 N
Q.4 :
Find the gravitational force of attraction between a man of mass of 50 kg and a bus of mass 1500 kg, if the distance between them is 10 m.
Solution:
Given: m1 = 50 kg, m2 = 1500 kg, r = 10 m
The formula for gravitational force is given as:
F = Gm1m2/r2
Here, G = 6.67 ×10−11N⋅ m2/kg2
Substituting the values in the formula, we have:
F = 6.67×10−11N⋅m2/kg2)(1500kg)(50kg)/102
F = 5.0025 × 10-8 N
Q.5 :
Suppose the gravitational force between two bodies at a certain distance is 4 N. Find the force of attraction if the distance between them is doubled.
Solution:
Newton’s law of gravitation states that the gravitational force between two point like objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
F = Gm1m2/r2
Above equation shows that, for given masses, if r is replaced by 2r, the force becomes 1/4th original force.
Therefore ,force of attraction will become 4/4 =1 N.
Q.6 :
The mass of the Earth is 6 × 1024 kg. The distance between the Earth and the Sun is 1.5 × 1011m. If the gravitational force between the two is 3.5 × 1022N, what is the mass of the Sun?
Solution:
Given: me = 6 × 1024 kg, r = 1.5 × 1011 m and F = 3.5 × 1022 N
Formula for gravitational force is given as:
F = Gm1m2/r2
⇒ 3.5 × 1022 N =6.67×10−11×6×1024×msun/(1.5×1011)2
⇒ Mass of sun = = 1.967 × 1030 kg
Important Questions-Answers on Force of Gravitation Formula
Q1: Define Gravitational Force.
The gravitational force is a force that attracts any two objects in the universe, whether they have equal masses or not. Furthermore, Newton’s Universal Law of Gravitation states that everything, including you, pulls every other object in the universe.
Q2: What is Gravitational Force between two objects?
The Gravitational force between the two objects of masses m1 and m2 at a distance r apart from each other can be calculated by using the formula mentioned below:
F = Gm1m2 / r2
Q3: Who discovered Gravitational Force?
English mathematician Isaac Newton made the first discovery of gravitational laws and forces.
Q4: What are Two Properties of Gravitational Force?
The following are the important properties of gravitational forces:
- Gravitational forces are always attractive and the weakest of all the fundamental forces.
- It is a type of Non-Contact Force, as it does not require any physical contact or touch to be experienced by a system of objects.
Q5 : Will your weight be constant when you are travelling to Greenland from Brazil?
No, it will increase. As the acceleration due to gravity is greater at the poles and lesser at the equator, because of the bulged oblate shape of the earth, we will feel heavier at Greenland. (Greenland is closer to the North Pole, and Brazil is closer to the equator).
Q6 : Can you screen the effect of gravitation by any material medium?
No, the gravitational effect cannot be screened, unlike electrostatic force, because the gravitational force does not depend on any medium.
Q7 : Why are space rockets launched eastward?
The Earth spins (rotates) from west to east in 24 hours. If the space rockets are launched in the same direction, the relative velocity of the rocket increases, which helps it to rise without much fuel.
Q8 : Why does a bouncing ball bounce higher on hills than on planes?
As the altitude increases, the acceleration due to gravity decreases. Therefore, the ball bounces higher in hills than on planes.
Q9 : The gravitational potential energy is negative. Why?
The reference point of zero potential energy is at infinity, and the gravitational force is always attractive. Therefore, the gravitational potential energy, which is the negative of work done, is always negative.
Q10 : Why is Newton’s law of gravitation called universal law?
Newton’s law of gravitation holds good irrespective of the nature of the interacting bodies at all places and at all times.
Q11 : What is the weight of the body at the centre of the Earth?
The weight of the body at the centre of the earth is zero.
W = mg = 0
(g at the centre of the earth is zero).
Q12 : Does friction arise due to gravitation?
Friction does not arise due to gravitation. Its origin is electrical in nature.
Q13: What is the magnitude of the Gravitational Force?
The magnitude of the gravitional force between the earth and a 1 kg object is 9.8 N.
Q14 : What is the Range of Gravitational Force?
The range of the gravitational force is infinite.
