Advertisements
Advertisements
Question
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.
Solution
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
RELATED QUESTIONS
What is the importance of the universal law of gravitation?
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?
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.
Four particles of equal masses M move along a circle of radius R under the action of their mutual gravitational attraction. Find the speed of each particle.
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 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.
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:
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 |
State the universal law of gravitation and derive its mathematical expression.
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?
