Gravitation

Physics Part I

Physics

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The earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the earth. The escape velocity of a body from this platform is fv_{e}, where v_{e} is its escape velocity from the surface of the earth. The value of f is

B.

If energy in the form of kinetic energy which is equal to binding energy, is supplied to the sphere, it leaves the gravitational field of earth.

At a platform at a height h,

escape energy = binding energy of sphere

or

But at surface of earth,

As given,

Hence,

If energy in the form of kinetic energy which is equal to binding energy, is supplied to the sphere, it leaves the gravitational field of earth.

At a platform at a height h,

escape energy = binding energy of sphere

or

But at surface of earth,

As given,

Hence,

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Is Geodesic always a straight line?

No, Geodesic is a straight line if and only if, the two points lie on the flat surface. If the two points lie on the curved surface then it is a curved line.

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What is Geocentric theory?

According to the geocentric theory, all the astronomical bodies like the moon, the sun and stars revolve around the earth, and the earth is at the centre of the universe.

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What is the celestial sphere?

At night, if we see the planets and the stars in the sky, all appear to lie in the hemisphere (rest of the hemisphere we are unable to see because of being on the other side of the earth). This sphere is called the celestial sphere.

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What is Heliocentric theory?

According to the Heliocentric theory, the sun is at the centre and various planets revolve around the sun at their axis.

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The position co-ordinates of two particles of masses m_{1} and m_{2}are (x_{1}, y_{1}, z_{1}) and (x_{2}, y_{2}, z_{2}) respectively. Find the coordinates of the centre of mass.

The position vectors of masses m

Let the position coordinates of the centre of mass be (X, Y, Z).

Therefore the position vector of centre of mass is,

Since,

Comparing the coefficients of , we get

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