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6.2 Gravitational field and gravitational field strength (SB p. 203)
Unit – N kg-1
The gravitational field strength (g) at a point in a gravitational field is defined as the gravitational force of attraction per unit mass at that point.
mFg
g
Mass
force nalGravitatio )(strength field nalGravitatio
On the earth or other planets, the gravitational field lines are radially inward (radial field). The parallel field lines indicate that it is a uniform field.
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6.2 Gravitational field and gravitational field strength (SB p. 203)
Other than the earth, the gravitational field strength (g) of a point at a distance r from the centre of an isolated sphere of mass M is also equal to:
2rMGg
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6.2 Gravitational field and gravitational field strength (SB p. 204)
Q:Q: The mass of the earth is approximately 80 times that of the moon and the earth’s radius is 3.7 times that of the moon. If the acceleration of free fall on the earth is 9.81 m s−2, estimate the gravitational field strength (g) on the moon’s surface.
Solution
6.2 Gravitational field and gravitational field strength (SB p. 205)
Q:Q: A space capsule travels from the earth towards the moon. Calculate its distance from the earth where it is under zero gravity. (Consider only the gravity due to the earth and the moon.)
(Mass of earth ME = 5.98 × 1024 kg; mass
of moon MM = 7.35 × 1022 kg; distance
between centre of earth and centre of moon = 3.84 × 108 m.) Solution
6.2 Gravitational field and gravitational field strength (SB p. 205)
Q:Q: A certain star of mass M and radius r rotates so rapidly that materials at its equator only just remain on its surface. Given that the gravitational constant is G, find the period of self-rotation of the star in terms of G, M and r.
Solution
6.2 Gravitational field and gravitational field strength (SB p. 206)
m and the acceleration due to gravity at the earth’s surface is 9.81 m s−2. Find the acceleration of free fall at a height of 6.38 × 104 m from the earth’s surface.
Solution
6.2 Gravitational field and gravitational field strength (SB p. 209)
1. In the case of a shell and a particle outside the shell, the shell attracts the particle as if all the mass of the shell were concentrated at its centre.
2. If the particle is inside the shell, the net force acted on the particle is zero.
6.2 Gravitational field and gravitational field strength (SB p. 209)
In the calculation, the gravitational force is assumed to be the same everywhere on the earth. Therefore, the centripetal force is affected by latitude only.
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6.2 Gravitational field and gravitational field strength (SB p. 212)