Question

A planet of mass $M$, has two natural satellites with masses $m_{1}$ and $m_{2}$. The radii of their circular orbits are $R_{1}$ and $R_{2}$ respectively. Ignore the gravitational force between the satellites. Define $v_{1}, L_{1}, K_{1}$ and $T_{1}$ to be, respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite 1 ; and $v_{2}, L_{2}, K_{2}$ and $T_{2}$ to be the corresponding quantities of satellite 2. Given $m_{1} / m_{2}=2$ and $R_{1} / R_{2}=1 / 4$, match the ratios in List-I to the numbers in List-II.

LIST-I
(P) $\frac{v_{1}}{v_{2}}$
(Q) $\frac{L_{1}}{L_{2}}$
(R) $\frac{K_{1}}{K_{2}}$
(S) $\frac{T_{1}}{T_{2}}$

LIST-II
(1) $\frac{1}{8}$
(2) 1
(3) 2
(4) 8

Accepted Answer

(B) $\mathbf{P} \rightarrow \mathbf{3} ; \mathbf{Q} \rightarrow \mathbf{2} ; \mathbf{R} \rightarrow \mathbf{4} ; \mathbf{S} \rightarrow \mathbf{1}$

Answer

(A) $\mathbf{P} \rightarrow \mathbf{4} ; \mathbf{Q} \rightarrow \mathbf{2} ; \mathbf{R} \rightarrow \mathbf{1} ; \mathbf{S} \rightarrow \mathbf{3}$

Answer

(C) $\mathbf{P} \rightarrow \mathbf{2} ; \mathbf{Q} \rightarrow \mathbf{3} ; \mathbf{R} \rightarrow \mathbf{1} ; \mathbf{S} \rightarrow \mathbf{4}$

Answer

(D) $\mathbf{P} \rightarrow \mathbf{2} ; \mathbf{Q} \rightarrow \mathbf{3} ; \mathbf{R} \rightarrow \mathbf{4} ; \mathbf{S} \rightarrow \mathbf{1}$

JEE Advanced · 2018 · 20 May 2018 · Paper 2 · Gravitation

Solution

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