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
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?
Choose the correct alternative:
Acceleration due to gravity increases/decreases with increasing depth. (assume the earth to be a sphere of uniform density).
State Kepler’s law which is represented by the relation r3 ∝ T2.
Which of the Kepler’s laws of planetary motion led Newton to establish the inverse-square rule for gravitational force between two bodies ?
Suppose the gravitational potential due to a small system is k/r2 at a distance r from it. What will be the gravitational field? Can you think of any such system? What happens if there were negative masses?
Which of the following quantities remain constant in a planetary motion (consider elliptical orbits) as seen from the sun?
The mass of moon is about 0.012 times that of earth and its diameter is about 0.25 times that of earth. The value of G on the moon will be:
Explain the following:
People often shake the branches of a tree for getting down its fruits.
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 .
Multiple Choice Question. Select the correct option.
The mass of earth is 6 × 1024 kg and radius of earth is 6.4 × 106 m. The magnitude of force between the mass of 1 kg and the earth is:
You can change the direction in which an object is moving by___________.
Name and state the action and reaction in the following case:
A book lying on a table.
The ______ force is much weaker than other forces in nature.
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 ______.
Newton's universal law of gravitation applies to ______.
The acceleration of the Moon towards the Earth is approximately ______.
Newton formulated the Universal Law of Gravitation by combining the ideas of which two scientists with his own Laws of Motion?
