Advertisements
Advertisements
प्रश्न
Answer the following question.
State Newton’s law of gravitation and express it in vector form.
उत्तर
- 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
संबंधित प्रश्न
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?
If the moon attracts the earth, why does the earth not move towards the moon?
Answer the following:
An astronaut inside a small space ship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size, can he hope to detect gravity?
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).
How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around the sun is 1.5 × 108 km.
State and explain Kepler's laws of planetary motion. Draw diagrams to illustrate these laws.
A person brings a mass of 1 kg from infinity to a point A. Initially the mass was at rest but it moves at a speed of 2 m s −1 as it reaches A. The work done by the person on the mass is −3 J. The potential at A is
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.
A body is suspended from a spring balance kept in a satellite. The reading of the balance is W1 when the satellite goes in an orbit of radius R and is W2 when it goes in an orbit of radius 2 −R.
Three equal masses m are placed at the three corners of an equilateral triangle of side a. Find the force exerted by this system on another particle of mass m placed at (a) the mid-point of a side, (b) at the centre of the triangle.
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.
Derive an expression for the gravitational field due to a uniform rod of length L and mass M at a point on its perpendicular bisector at a distance d from the centre.
A tunnel is dug along a chord of the earth at a perpendicular distance R/2 from the earth's centre. The wall of the tunnel may be assumed to be frictionless. Find the force exerted by the wall on a particle of mass m when it is at a distance x from the centre of the tunnel.
The acceleration produced by a force in an object is directly proportional to the applied _________ And inversely proportional to the _________ Of the object.
Distinguish between gravity and gravitation
A ball is thrown up with a speed of 4.9 ms-1.
Calculate the time it takes to reach this height.
A ball is thrown up with a speed of 4.9 ms-1.
Prove that the time of ascent is equal to the time of descent.
What is meant by the equation :
`g= Gxxm/r^2`
where the symbols have their usual meanings.
What does a force do in the following case?
You catch a kicked ball.
Is there a gravitational attraction between you and the book? Explain.
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.
Calculate the acceleration due to gravity at a height of 300 km from the surface of the Earth. (M = 5.98 × 1024 kg, R = 6400 km).
State the universal law of gravitation and derive its mathematical expression.
The force of gravitation between two bodies of mass 1 kg each separated by a distance of 1 m in vacuum is ____________.
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.