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

Answer 1

The correct option is 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

The field is found to be linearly proportional to the distance until r=R and is given by $g=GMx/R^3$.
For r=0 to r=R, g varies as a straight line.
Substituting $M=\rho \left(4\pi R^3\right)/3$ in the expression for g, we get, $g=Gx4\pi \rho /3⟹\left(g/x\right)=4G\pi \rho /3$.
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)