Advertisements
Advertisements
Question
Answer the following question.
State Newton’s law of gravitation and express it in vector form.
Solution
- Statement:
Every particle of matter attracts every other particle of matter with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. - In vector form, it can be expressed as,
`vec"F"_21 = "G" ("m"_1"m"_2)/"r"^2(- hat"r"_21)`
where, `hat"r"_21` is the unit vector from m1 to m2. The force `vec"F"_21` is directed from m2 to m1.
APPEARS IN
RELATED QUESTIONS
The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?
Choose the correct alternative:
Acceleration due to gravity is independent of mass of the earth/mass of the body.
Which of the Kepler’s laws of planetary motion led Newton to establish the inverse-square rule for gravitational force between two bodies ?
Can you think of two particles which do not exert gravitational force on each other?
A tunnel is dug along a diameter of the earth. Find the force on a particle of mass m placed in the tunnel at a distance x from the centre.
Explain the following:
People often shake the branches of a tree for getting down its fruits.
Write an expression for the gravitational force of attraction between two bodies of masses m1 and m2 separated by a distance r.
A ball is thrown vertically upwards. It goes to a height 20 m and then returns to the ground. Taking acceleration due to gravity g to be 10 ms-2, find: the initial velocity of the ball.
Define one Newton. How much maximum acceleration can it produce in a mass of 1 kg?
Who stated the law of gravitation?
How will the force of gravitation between two objects change if the distance between them is:
Almost zero
All objects in the universe attract each other along the line joining their________.
Is the law of gravitation applicable in case of the sun and the moon?
What does a force do in the following case?
You pull the skin of your arm
Name and state the action and reaction in the following case:
A person walking on the ground.
State the law of gravitation. Why is it called universal?
State Newton's law of gravitation. What is the difference between:
Gravity and gravitation
Show that gravity decreases at higher altitudes.
Solve the following problem.
Find the gravitational force between the Sun and the Earth.
Given Mass of the Sun = 1.99 × 1030 kg
Mass of the Earth = 5.98 × 1024 kg
The average distance between the Earth and the Sun = 1.5 × 1011 m.
The value of universal gravitational constant (G) in the SI unit is ______.
State Newton's universal law of gravitation. Express it with the mathematical form of force of gravitation?
Three uniform spheres, each having mass m and radius r, are kept in such a way that each touches the other two. The magnitude of the gravitational force on any sphere due to the other two is
Choose the wrong option.
If the law of gravitation, instead of being inverse-square law, becomes an inverse-cube law- ______.
- planets will not have elliptic orbits.
- circular orbits of planets is not possible.
- projectile motion of a stone thrown by hand on the surface of the earth will be approximately parabolic.
- there will be no gravitational force inside a spherical shell of uniform density.
We can shield a charge from electric fields by putting it inside a hollow conductor. Can we shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?
The gravitational force between a hollow spherical shell (of radius R and uniform density) and a point mass is F. Show the nature of F vs r graph where r is the distance of the point from the centre of the hollow spherical shell of uniform density.
Give scientific reasons for the following:
Newton's gravitational law is the universal law of gravitation.
Complete the chart below.
| F(N) | M1(kg) | M2(kg) | D(m) |
| (a) | 50 | 84 | 02 |
| 16 × 109 | 1.63 × 1022 | (b) | 34 |
Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If `sqrt8` R is the distance between the centres of a ring (of mass 'm')and a sphere (mass 'M') where both have equal radius 'R'.
