Question

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

A

the slope of the curve from r=0 to r=R is a straight line with slope being proportional to density of the object

B

the slope of the curve from r=0 to r=R is a straight line with slope = g

C

the slope of the curve from r=0 to r=R is a straight line with slope = 0

D

the slope of the curve from r=0 to r=R is a straight line with slope = GM

Medium
Solution
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Correct option is A)

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

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

Substituting in the expression for g, we get,

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)

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