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# Category Archives: Gravitation

## Motion under gravity

When two bodies of two different weights(ex..an elephant n a boy) falling from certain height.. Both reaches the ground at the same time because gravity is independent of mass…but when we leave a leaf n a coin from a certain height coin reaches the ground first why?

It is the air resistance which plays the VILLAIN’s role here. The leave is affected more by the air resistance than the coin. In other words the magnitude of force exerted by gravity on ball is much greater than buoyant force and air resistance in the case of the coin whereas in the case of a leaf, the air resistance and buoyant force is comparable to its weight.

If these are dropped in a vacuum chamber, both will fall together and will take the same interval of time to reach the ground when dropped from the same height.

Please refer to the following videos

## A problem from Gravitation

Three identical bodies each of mass m are located at the vertices of an equilateral triangle with side r. At what speed they move if they all revolve under the influence of one another’s gravitation in a circular orbit circumscribing the triangle while still preserving the equilateral triangle

## Variation in acceleration due to gravity (g) with depth

As we go deeper from the earth suface the gravity starts decreasing but formulla is ‘F=G*m*M/r2 where distance between the object and the earth is r2 which is inversally proportional to the ‘g’ then why as we go deeper from the earth suface the gravity starts decreasing; it should be increased because distance between the earth and the object is less. but it start decreasing why?

When we go deeper into earth, the attraction at that point is due to a sphere of earth of radius (R – d) where d is the depth below the surface of earth.

Let a body of mass m be kept on the surface of earth. The force exerted by earth on it,

$F_{surface}=mg=\frac{GMm}{R^{2}}$ where M is the total mass of earth and R is the radius of earth.

But, $M&space;=&space;\frac{4\pi&space;R^{3}\rho&space;}{3}$

Substituting for M,

$mg&space;=&space;\frac{4\pi&space;G\rho&space;m&space;R}{3}$

or  (more…)

## GPS (Global Positioning System) Accuracy of Measurement

The 24 satellites that orbit the earth and define the Global Positioning System use
precision atomic clocks that are accurate to 1 x 10-9 s, or 1 nanosecond (1ns). A person on the earth, using their mobile phone, can usually “see” 4-12 of the 24 satellites at any one time.

The satellites are moving, relative to the surface of the earth, at 1.4 x 104 km/h.
a- Calculate  for one of these satellites,
Civilian GPS measurements have to be accurate at the level of 5-10m. How accurate must our knowledge of the clocks on the satellites be in order to achieve this level of accuracy in our position measurement?
[HINT: light signals are used by your phone and the satellites to perform the triangulation]
c-If we measure the passage of 1 day on earth using a clock that is identical to the clocks on the GPS satellites, how much time have the clocks on the satellites measured? What about for the passage of 2 days on earth? For this problem, it will be useful to apply the Binomial Expansion again

## Is the gravitational force between moon & earth are equal ?

Is the gravitational force between moon & earth are equal ?

If the question is- “Is the force exerted by earth on moon is equal to the force exerted by moon on earth?” then the answer is “Yes

I hope that more questions will follow.

• Comparison of charge and mass

## Gravity at different places on earth

The centre of earth is equator and if equator is the centre of earth and as we know the gravity is maximum at centre of the earth then why the gravity is less there?

(Evidently, the question is posted out of some misconception or confusion)

Centre of earth means the centre INSIDE THE EARTH, and there the value of g is zero.

At the equator, the distance from the centre is maximum and therefore g is the minimum. Further, the effect of rotation is maximum at the equator as the distance of any particle on the surface is farthest from the axis of rotation at the equator and any object at the equator requires maximum centripetal force which is derived from the gravitational force of earth. Thus in both ways, g is minimum at the equator.

## Newton’s Law of Gravitation and Acceleration due to gravity

According to Newton’s law, force produce acceleration, this acceleration depends on the mass, larger the mass lower will be the acceleration. But in the case of Earth’s gravity, acceleration is the same for every object.why?(forget equations for a moment and the conceptually)

” the force with which the earth pulls a body towards it is equal to the weight of the body (mg), so heavy objects are pulled by greater force and lighter one with small.. so acceleration is same.”

See the full discussion at https://www.facebook.com/groups/haibuddys/469860503040637

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