﻿ 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 fve, where ve is its escape velocity from the surface of the earth. The value of f is from Physics Gravitation Class 11 Manipur Board

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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 fve, where ve 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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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?

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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 m1 and m2are (x1, y1, z1) and (x2, y2, z2) respectively. Find the coordinates of the centre of mass.

The position vectors of masses m1 and m2 are respectively,

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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