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Gravitational Potential

Two satellite...

Question

Two satellite having masses $M_{1}$ and $M_{2}$ $(M_{1} = \frac{M_{2}}{2})$ are moving in circular orbits with orbital speed $v_{1}$ and $v_{2}$ respectively. If $v_{1} = 2 v_{2}$ then ratio of their time periods is :

A

1 : 4

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B

1 : 8

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C

1 : 16 \sqrt{2}

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D

1 : 16

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Solution

The correct option is B $1 : 8$

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Similar questions

Q. Two satellites of masses

m_{1}

m_{2}

m_{1}

m_{2}

) are revolving round the earth in circular orbits of radii

r_{1}

r_{2}

r_{1}

r_{2}

) respectively. Which of the following statements is true regarding their speeds

v_{1}

v_{2}

v_{1}

?

Q. A planet of mass M, has two natural satellites with masses

m_{1}

m_{2}

. The radii of their circular orbits are

R_{1}

R_{2}

respectively. Ignore the gravitational force between the satellites. Define

v_{1}, L_{1}, K_{1}

T_{1}

to be respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite

1

v_{2}, L_{2}, K_{2}

T_{2}

to be the corresponding quantities of satellite

2

m_{1} / m_{2} = 2

R_{1} / R_{2} = 1 / 4

, match the ratios in List - I to the numbers in List-II.

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. $8$

Q. Two artificial satellite of masses

m_{1}

m_{2}

m_{1} > m_{2}

) are revolving round the earth in circular orbits of radii

r_{1}

r_{2}

r_{1} > r_{2}

) respectively. Which of the following statements is true regarding their speed

v_{1}

v_{2}

Q. Two satellites of masses m1 and m2 (m1 > m2) are revolving round the earth in circular orbits of radii r1 and r2 (r1 > r2) respectively. Which of the following statements is true regarding their speeds v1 and v2 ?

Q. A planet of mass

M

, has two natural satellites with masses

m_{1}

m_{2}

. The radii of their circular orbits are

R_{1}

R_{2}

respectively. Ignore the gravitational force between the satellites. Define

v_{1}

L_{1}

K_{1}

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}

T_{2}

to be the corresponding quantities of satellite 2. Given

m_{1} / m_{2} = 2

R_{1} / R_{2} = 1 / 4

, match the ratios in List - I to the numbers in List-II.

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