Question

Consider two solid spheres of radii $R, = 1m, \,R_2 = 2m$ and masses $M_1$ and $M_2$, respectively. The gravitational field due to sphere (1) and (2) are shown. The value of $\frac{m_{1}}{m_{2}}$ is :

• A. $\frac{2}{3}$
• B. $\frac{1}{6}$
• C. $\frac{1}{2}$
• D. $\frac{1}{3}$

Answer 1

Answer: (B)

$\frac{1}{6}$

Answer 2

Gravitational field on the surface of a solid
sphere $I_{g}=\frac{GM}{R^{2}}$
By the graph
$\frac{GM_{1}}{\left(1\right)^{2}}=2$
and $\frac{GM_{2}}{\left(2\right)^{2}}=3$
On solving
$\frac{M_{1}}{M_{2}}=\frac{1}{6}$