A plot of gravitational field v/s distance of a point from the center for a solid sphere of radius R revealed

Question

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Answer 1

The field is found to be linearly proportional to the distance until r=R and is given by $g = G M x / R^{3}$ .

For r=0 to r=R, g varies as a straight line.

Substituting $M = ρ (4 π R^{3}) / 3$ in the expression for g, we get, $g = G x 4 π ρ / 3 ⟹ (g / x) = 4 G π ρ / 3$ .

We also know that G/x gives the slope of the straight line.

Hence slope is proportional to the density of the object

The correct option is (a)

Answer 2

The field is found to be linearly proportional to the distance until r=R and is given by

g = G M x / R^{3}

.

For r=0 to r=R, g varies as a straight line.

Substituting

M = ρ (4 π R^{3}) / 3

in the expression for g, we get,

g = G x 4 π ρ / 3 ⟹ (g / x) = 4 G π ρ / 3

.

We also know that G/x gives the slope of the straight line.

Hence slope is proportional to the density of the object

The correct option is (a)