Gravitation

Physics Part I

Physics

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Choose the correct answer from among the given ones:Â

For the problem 8.10, the direction of the gravitational intensity at an arbitrary point P is indicated by the arrow (i) d, (ii) e, (iii) f, (iv) g.Â

Hence, the correct answer is (ii).

Gravitational potential (*V*) is constant at all points in a spherical shell. Hence, the gravitational potential gradient (*dV*/*dR*) is zero everywhere inside the spherical shell. The gravitational potential gradient is equal to the negative of gravitational intensity. Hence, intensity is also zero at all points inside the spherical shell. This indicates that gravitational forces acting at a point in a spherical shell are symmetric.Â

Gravitational potential (

If the upper half of a spherical shell is cut out (as shown in the given figure), then the net gravitational force acting on a particle at an arbitrary point P will be in the downward direction.

Since gravitational intensity at a point is defined as the gravitational force per unit mass at that point, it will also act in the downward direction. Thus, the gravitational intensity at an arbitrary point P of the hemispherical shell has the direction as indicated by arrowÂ

Â

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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.Â

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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 theÂ celestial sphere.

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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.Â

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The position co-ordinates of two particles of masses m_{1}Â 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, Â Â

Â

Comparing the coefficients of Â , we get

Â

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