Gravitation

Answer (c) Both A & B are true

Answer (d) When the range is long, gravitational force becomes repulsive.

The time period of an artificial satellite is given by where is radius of earth and the height of satellite. From the above formula it is clear that time period of revolution does not depend upon the mass of the satellite.

Acceleration due to gravity at the center of the earth is zero. Time period of a simple pendulum is given by, So time period at the centre of the earth becomes infinite.

Answer (d) is equal to the period of rotatiohof the earth about its axis

Weak nuclear forces make the atom unstable. So, the atoms decay to attain stability.

Clearly from above expressions we have a decrease in force by .

The earth revolves around the sun due to gravitation pull of the sun. Due to this gravitational attraction between this celestial body, centripetal force is generated which binds the solar system together. Hence revolution of earth round the sun is the evidence to show that there ust be force acting on earth nd directed towards the sun.

It's because the pull from every direction is exactly the same. This is obvious from the center, but as you move to one side, you're closer to that side, which increases its pull, but this is exactly offset by the fact that there's now MORE mass on the other side.

The forces that bind fermions (electron, proton, neutron) together are termed weak forces, whereas the forces that bind the constituents of a nucleus are strong nuclear forces.

The forces that bind fermions (electron, proton, neutron) together are termed as weak forces. Whereas the forces that bind the constituents of a nucleus are strong nuclear force.

Answer (b) Electro magnetic Forces

The universal gravitational constant is of the order making it the weakest forces compared to the rest. Gravitation range to infinity. However, it is the weakest of the fundamental forces. The gravitational strength is only of the strength of the strongest nuclear force.

Electromagnetic force: The relative strength of the electromagnetic force is of the strong nuclear force. Its force drops off as the square of the separation between charged particles or magnetic poles, although the range is infinite.
Nuclear force: The relative strength of the strong force is designated as 1 . The range of this force is small, approximately . Apparently, this force does not decrease by the inverse square as do the gravitational and electromagnetic forces. Instead, it just stops at its given separation.
Electrostatic force: Electrostatic force is not a natural occurring force. The weak form of electrostatic force can be generated by rubbing ebonite with flannel. Even though electrostaticaly induced forces seem to be rather weak, the electrostatic force between an electron and a proton, that together make up a hydrogen atom, is about 36 orders of magnitude stronger than the gravitational force acting between them.

Due to the negative sign, when the radius is halved the potential decreases.

Answer (a)

Let be the speed of the body when it is at infinite distance from the centre of the Earth and u be speed of projection of the body from the earth's surface
According to law of conservation of mechanical energy,

or,

Escape velocity of a planet


For same

Here,

or,

We know,
Since G and M are constants, so g increases as R decreases

As
So,

Acceleration due to gravity of the Earth is given by
or (for same mass)
If the Earth shrinks in its size, mass remaining same, the value of g on its surface will increase.

Potential energy of mass on the surface of the earth, .
Potential energy of mass at a distance above the surface of the earth,
Here,

Increase in potential energy of mass, m

Weight of body;
Here, g is acceleration due to gravity which is maximum on the surface of the earth.

Acceleration due to gravity at a height
from the earth's surface is
where g is acceleration due to gravity on the earth's surface.
At

For a given planet,
Gravitational field strength at the surface of another planet,
Here,

Weight of a mass depends on the acceleration due to gravity .
Acceleration due to gravity at height from the surface of earth
....(i)
Acceleration due.to gravity at depth from the surface of earth

.....(ii)
Required ratio =

For a satellite in a stable circular orbit: - Kinetic Energy: - Potential Energy: Dividing: So,

The acceleration due to gravity at the poles remains the same regardless of Earth's rotation speed. This is because, at the poles, the centripetal acceleration caused by the Earth's rotation is zero. Therefore, the only factor affecting gravity at the poles is the Earth's mass, not its rotational speed. Thus, the correct answer is (C).

In this case, the modulation index is determined from the maximum amplitude of the message signal and the amplitude of the carrier wave . The modulation index is defined as: Given: - , - , We can substitute these values into the equation to get: Thus, the modulation index is , so the correct answer is (B).

The acceleration due to gravity at a height above the Earth's surface is given by the formula: where:
- is the acceleration due to gravity at height ,
- is the acceleration due to gravity at the surface of the Earth,
- is the radius of the Earth,
- is the height above the Earth's surface. We are given that (1 percent of the surface value). Substituting this into the equation: Dividing both sides by : Taking the reciprocal of both sides: Taking the square root of both sides: Solving for :
Thus, the height is: Therefore, the correct answer is:

The acceleration due to gravity at the Earth's surface is influenced by the Earth's shape and rotation. The value of gravity is not constant everywhere on Earth due to two main factors:
1. The Earth is not a perfect sphere, but an oblate spheroid. The centrifugal force due to the Earth's rotation is greater at the equator than at the poles, which reduces the effective gravitational force at the equator.
2. The radius of the Earth is greater at the equator than at the poles, and gravity decreases with distance from the Earth's center. At the poles ( ), gravity is unaffected by centrifugal force, and it has the maximum value. At the equator ( ), the centrifugal force due to the Earth's rotation reduces the effective force of gravity. This results in gravity at the equator being slightly less than gravity at the poles.
Thus, the acceleration due to gravity is: Hence, the correct relationship is , and the answer is .