JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Gravitation

The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is

9 : 4

. The mass of the planet is

\frac{1}{9}

th of that of the Earth. If '

R

' is the radius of the Earth, what is the radius of the planet ? (Take the planets to have the same mass density)

(A) $\frac{R}{3}$
(B) $\frac{R}{4}$
(C) $\frac{R}{9}$
(D) $\frac{R}{2}$ ✓ Correct

Answer: (D)

Solution

Surface weight is

\frac{GM m}{r ^{2}}

, so the ratio of weights is

\frac{M _{E} / R ^{2}}{M _{P} / r _{P}^{2}} = \frac{9}{4}

. Putting

M_{P} = \frac{M _{E}}{9}

turns this into

\frac{9 r _{P}^{2}}{R ^{2}} = \frac{9}{4}

, so

\frac{r _{P}^{2}}{R ^{2}} = \frac{1}{4}

and

r_{P} = \frac{R}{2}

JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Single correct option

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