JEE PYQ: Gravitation Question 31
Question 31 - 2020 (08 Jan Shift 1)
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:
(1) $\frac{2}{3}$
(2) $\frac{1}{6}$
(3) $\frac{1}{2}$
(4) $\frac{1}{3}$
Show Answer
Answer: (2)
Solution
From the graph, $E_1$ at surface of sphere 1 is $\frac{2}{3}$ of $E_2$ at surface of sphere 2. $\frac{GM_1}{R_1^2} = \frac{2}{3}\frac{GM_2}{R_2^2}$. $\frac{M_1}{M_2} = \frac{2}{3} \times \frac{R_1^2}{R_2^2} = \frac{2}{3} \times \frac{1}{4} = \frac{1}{6}$.
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