Gravitation
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 ListI to the numbers in ListII.
LIST–I  LIST–II  
P.  $\frac{{v}_{1}}{{v}_{2}}$  1.  $\frac{1}{8}$ 
Q.  $\frac{{L}_{1}}{{L}_{2}}$  2.  1 
R.  $\frac{{K}_{1}}{{K}_{2}}$  3.  2 
S.  $\frac{{T}_{1}}{{T}_{2}}$  4.  8 
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JEE Advanced 2018
In columnI list of different objects is given, in columnII, a list of Er graphs (variation of gravitational field with distance from centre of object), and in columnIII a list Vr graphs (Variation of gravitational potential with distance from centre of object) are given
(Curves are approximate not subjected to scale)
Which of the following options correctly matches gravitational field variation and gravitational potential variation for a circular ring
(Curves are approximate not subjected to scale)
ColumnI  ColumnII  ColumnIII  
(I)  (i)  (P)  
(II)  (ii)  (Q)  
(III)  (iii)  (R) 


(IV)  (iv)  (S) 
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JEE Advanced 0
In columnI list of different objects is given, in columnII, a list of Er graphs (variation of gravitational field with distance from centre of object), and in columnIII a list Vr graphs (Variation of gravitational potential with distance from centre of object) are given
(Graphs are just approximate curves not according to scale)
Which of the following options correctly matches gravitational field variation and gravitational potential variation for a spherical shell?
(Graphs are just approximate curves not according to scale)
ColumnI  ColumnII  ColumnIII  
(I)  (i)  (P)  
(II)  (ii)  (Q)  
(III)  (iii)  (R) 


(IV)  (iv)  (S) 
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JEE Advanced 0
In columnI list of different objects is given, in columnII, a list of Er graphs (variation of gravitational field with distance from centre of object), and in columnIII a list Vr graphs (Variation of gravitational potential with distance from centre of object) are given
(Graphs are just approximate curves not according to scale)
Which of the following options correctly matches variation of gravitational field and potential for solid sphere?
(Graphs are just approximate curves not according to scale)
ColumnI  ColumnII  ColumnIII  
(I)  (i)  (P)  
(II)  (ii)  (Q)  
(III)  (iii)  (R) 


(IV)  (iv)  (S) 
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JEE Advanced 0
In the figure given below it is shown that a particle 'P' having position vector $\overrightarrow{r}$ with respect to centre of earth is projected such that its velocity v perpendicular to $\overrightarrow{r}$.
In table given below column I shows the magnitudes of velocity v and column II shows the trajectory taken by particle Match column I with Column II.
Column I  Column II  
P.  $v=\sqrt{\frac{2GM}{r}}$  1.  Circular 
Q.  $v=\sqrt{\frac{GM}{r}}$  2.  Parabolic 
R.  $\sqrt{\frac{GM}{r}}<v<\sqrt{\frac{2GM}{r}}$  3.  Elliptical 
S.  $v>\sqrt{\frac{2GM}{r}}$  4.  Hyperbolic 
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JEE Advanced 0