Question

If g represents the gravitational field due to a solid sphere of radius R, then a plot of $g{R}^3$ v/s R in the region from r=0 to r=R will be

• A. A straight line parallel to Y-axis
• B. A straight line parallel to X-axis
• C. A straight line passing through the origin, whose slope is GM
• D. A straight line passing through the origin, whose slope is g

Answer 1

The correct option is C A straight line passing through the origin, whose slope is GM

We know that field inside a solid sphere is given by $g=GMx/R^3⟹g{R}^3=GMx$
Thus a plot of $g{R}^3$ v/s x will give rise to a straight line , whose slope is GM

The correct option is (c)