Advertisements
Advertisements
Questions
Write the answer of the question with reference to laws of gravitation.
State the universal law of gravitation.
Answer the following question.
State Newton’s law of gravitation.
Advertisements
Solution
The universal law of gravitation states that every object in the universe attracts every other object with a force called the gravitational force. The force acting between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
F ∝ m M (masses of two bodies m and M)
F ∝ `1/"d"^2` (d is the distance between the two bodies.)
A and B are two bodies, the distance between which is given as d.
F = force with which one body is attracting the other.
G = proportionality constant.
APPEARS IN
RELATED QUESTIONS
Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.
What happens to the force between two objects, if the distance between the objects is doubled and tripled?
What happens to the force between two objects, if the masses of both objects are doubled?
Answer the following:
You can shield a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?
If you compare the gravitational force on the Earth due to the Sun to that due to the Moon, you would find that the Sun’s pull is greater than the Moon’s pull. (You can check this yourself using the data available in the succeeding exercises). However, the tidal effect of the Moon’s pull is greater than the tidal effect of Sun. Why?
Choose the correct alternative:
Acceleration due to gravity increases/decreases with increasing altitude.
Choose the correct alternative:
Acceleration due to gravity is independent of mass of the earth/mass of the body.
The gravitational intensity at the centre of a hemispherical shell of uniform mass density has the direction indicated by the arrow (see Fig 8.12) (i) a, (ii) b, (iii) c, (iv) 0.
Choose the correct answer from among the given ones:
For the problem 8.10, the direction of the gravitational intensity at an arbitrary point P is indicated by the arrow (i) d, (ii) e, (iii) f, (iv) g.
A rocket is fired from the earth towards the sun. At what distance from the earth’s centre is the gravitational force on the rocket zero? Mass of the sun = 2 ×1030 kg, mass of the earth = 6 × 1024 kg. Neglect the effect of other planets etc. (orbital radius = 1.5 × 1011 m).
State Kepler’s law which is represented by the relation r3 ∝ T2.
State the universal law of gravitation. Name the scientist who gave this law.
Write the three laws given by Kepler. How did they help Newton to arrive at the inverse square law of gravity?
At noon, the sun and the earth pull the objects on the earth's surface in opposite directions. At midnight, the sun and the earth pull these objects in same direction. Is the weight of an object, as measured by a spring balance on the earth's surface, more at midnight as compared to its weight at noon?
Let V and E represent the gravitational potential and field at a distance r from the centre of a uniform solid sphere. Consider the two statements:
(A) the plot of V against r is discontinuous.
(B) The plot of E against r is discontinuous.
Inside a uniform spherical shell
(a) the gravitational potential is zero
(b) the gravitational field is zero
(c) the gravitational potential is same everywhere
(d) the gravitational field is same everywhere
A semicircular wire has a length L and mass M. A particle of mass m is placed at the centre of the circle. Find the gravitational attraction on the particle due to the wire.
A solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in the following figure . A particle of mass m' is placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if (a) r < x < 2r, (b) 2r < x < 2R and (c) x > 2R.
A uniform metal sphere of radius a and mass M is surrounded by a thin uniform spherical shell of equal mass and radius 4a (In the following figure). The centre of the shell falls on the surface of the inner sphere. Find the gravitational field at the points P1 and P2 shown in the figure.
A particle of mass 100 g is kept on the surface of a uniform sphere of mass 10 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle away from the sphere.
The gravitational field in a region is given by \[E = \left( 2 \overrightarrow{i} + 3 \overrightarrow{j} \right) N {kg}^{- 1}\] . Show that no work is done by the gravitational field when a particle is moved on the line 3y + 2x = 5.
[Hint : If a line y = mx + c makes angle θ with the X-axis, m = tan θ.]
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 final velocity of the ball on reaching the ground .
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 total time of journey of the ball .
Distinguish between gravity and gravitation
All objects in the universe attract each other along the line joining their________.
The force of attraction between any two material objects is called __________.
Why don't you feel the force of attraction between your friend sitting close to you and yourself?
At what height above the earth's surface would the value of acceleration due to gravity be half of what it is on the surface? Take the radius of earth to be R.
What does a force do in the following case?
You pull the skin of your arm
What does a force do in the following case?
You twist a piece of rubber.
What does a force do in the following case?
You apply brakes to a running car.
What does a force do in the following case?
You catch a kicked ball.
Name and state the action and reaction in the following case:
A book lying on a table.
Name and state the action and reaction in the following case:
A person walking on the ground.
Why does a ball moving on a table top eventually stops?
What is the difference between gravity and gravitation?
Does the force of the earth's gravitation affect the motion of the moon? Explain your answer with reasons.
State Newton's law of gravitation. What is the difference between:
Gravity and gravitation
The distance-time values for an object moving along straight line are given below:
| Time (s) | Distance (m) |
| 0 | 0 |
| 1 | 1 |
| 2 | 8 |
| 3 | 27 |
Show that gravity decreases at higher altitudes.
Answer the following question.
What are the dimensions of the universal gravitational constant?
What do you mean by a gravitational constant?
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?
Give the applications of universal law gravitation.
For the weight of body of mass 5 kg to be zero on equator of the earth, angular velocity of the earth must be (The radius of earth = 6400 km, acceleration due to gravity = 10 m/s2).
The force of gravitation between two bodies of mass 1 kg each separated by a distance of 1 m in vacuum is ____________.
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
Particles of masses 2M, m and M are respectively at points A, B and C with AB = ½ (BC). m is much-much smaller than M and at time t = 0, they are all at rest (Figure). At subsequent times before any collision takes place ______.
How is the gravitational force between two point masses affected when they are dipped in water keeping the separation between them the same?
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.
Six point masses of mass m each are at the vertices of a regular hexagon of side l. Calculate the force on any of the masses.
Give scientific reasons for the following:
Newton's gravitational law is the universal law of gravitation.
Two particles of equal mass 'm' go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle with respect to its centre of mass is ______.
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'.
Ocean tides on Earth are mainly caused by:
The acceleration of the Moon towards the Earth is approximately:
