Q 11-07-168JEE MainJEE Main 2020 (8 Jan, Shift 1)Easy
Consider two solid spheres of radii $R_1 = 1$ m, $R_2 = 2$ m and masses $M_1$ and $M_2$, respectively. The gravitational fields due to spheres (1) and (2) are shown. The value of $\dfrac{M_1}{M_2}$ is:
Answer: (B) $\dfrac16$
For a solid sphere the field rises linearly inside and is largest at the surface, where $E = \dfrac{GM}{R^2}$.
Sphere 1: peak $2$ at $R_1 = 1$ m, so $GM_1 = 2\times1^2 = 2$.
Sphere 2: peak $3$ at $R_2 = 2$ m, so $GM_2 = 3\times2^2 = 12$.
$$\frac{M_1}{M_2} = \frac{2}{12} = \frac16$$
Solution by Sreeraj P, M.Sc Physics