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

JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Gravitation

Consider two solid spheres of radii

R_{1} = 1 m

R_{2} = 2 m

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) $\frac{1}{2}$
(B) $\frac{1}{3}$
(C) $\frac{1}{6}$ ✓ Correct
(D) $\frac{2}{3}$

Answer: (C)

Solution

The surface gravitational field of a uniform sphere is

g = \frac{GM}{R ^{2}}

. From the graph, sphere

1

has surface field

2

and sphere

2

has surface field

3

. For sphere

1

2 = \frac{G M _{1}}{1 ^{2}}

G M_{1} = 2

; for sphere

2

3 = \frac{G M _{2}}{2 ^{2}}

G M_{2} = 12

. The mass ratio is therefore

\frac{M _{1}}{M _{2}} = \frac{2}{12} = \frac{1}{6}

JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Single correct option

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