JEE PYQ: Gravitation Question 40
Question 40 - 2019 (12 Apr Shift 2)
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)
(1) $\frac{R}{3}$
(2) $\frac{R}{4}$
(3) $\frac{R}{9}$
(4) $\frac{R}{2}$
Show Answer
Answer: (4)
Solution
$\frac{W_e}{W_p} = \frac{g_e}{g_p} = \frac{9}{4}$. $\frac{GM_e/R^2}{GM_p/R_p^2} = \frac{9}{4}$. $\frac{M_e R_p^2}{M_p R^2} = \frac{9}{4}$. $\frac{9R_p^2}{R^2} = \frac{9}{4}$. $R_p = R/2$.
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