Solved Example Problems: Superposition principle for Gravitational field

EXAMPLE 6.3

a) Two particles of masses m1 and m2 are placed along the x and y axes respectively at a distance ‘a’ from the origin. Calculate the gravitational field at a point P shown in figure below.

Solution

Gravitational field due to m1 at a point P is given by,

Gravitational field due to m2 at the point p is given by,

The direction of the total gravitational field is determined by the relative value of m1 and m2.

When m1 = m2 = m

(iˆ + jˆ = jˆ + iˆ as vectors obeys commutation law).

total points  towards  the  origin  of  the co-ordinate system and the magnitude of total is Gm/a2. 

EXAMPLE 6.4

Qualitatively indicate the gravitational field of Sun on Mercury, Earth, and Jupiter shown in figure.

Since the gravitational field decreases as distance increases, Jupiter experiences a weak gravitational field due to the Sun. Since Mercury is the nearest to the Sun, it experiences the strongest gravitational field.