Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
a and c
Explanation:
If the law of gravitation becomes an inverse cube law. then we can write, for a planet of mass m revolving around the sun of mass M,
F = `(GMm)/a^3 = (mv^2)/a` .....(Where a is the radius of orbiting planet)
⇒ v = orbital speed = `sqrt(GM)/a`
⇒ `v ∝ 1/a`
Time period of revolution of a planet T = `(2πa)/v = (2πa)/(sqrt(GM)/a) = (2πa^2)/sqrt(GM)`
⇒ `T^2 ∝ a^4`
Hence, the orbit will not be elliptical. .....[For elliptical orbit T2 ∝ a3]
As force F = `((GM)/a^3)m = g m`
Where, `g^' = (GM)/a^3`
As g', acceleration due to gravity is constant, hence path followed by a projectile will be approximately parabolic. (as T ∝ a2)
APPEARS IN
संबंधित प्रश्न
How does the force of gravitation between two objects change when the distance between them is reduced to half?
If the moon attracts the earth, why does the earth not move towards the moon?
What happens to the force between two objects, if the distance between the objects is doubled and tripled?
Choose the correct alternative:
Acceleration due to gravity is independent of mass of the earth/mass of the body.
Can we apply Newton’s third law to the gravitational force ? Explain your answer.
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
A thin spherical shell having uniform density is cut in two parts by a plane and kept separated as shown in the following figure. The point A is the centre of the plane section of the first part and B is the centre of the plane section of the second part. Show that the gravitational field at A due to the first part is equal in magnitude to the gravitational field at B due to the second part.
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.
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.
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.
Where will you weigh more: at the moon's surface or at the earth's surface?
You can change the direction in which an object is moving by___________.
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
Complete the chart below.
| F(N) | M1(kg) | M2(kg) | D(m) |
| (a) | 50 | 84 | 02 |
| 16 × 109 | 1.63 × 1022 | (b) | 34 |
If the mass of one object is doubled and distance remains the same, the gravitational force will ______.
The acceleration of the Moon towards the Earth is approximately ______.
If the distance between two objects is doubled, the gravitational force becomes ______.
For an object outside a uniform solid sphere, from where is the sphere's mass considered to act?
