Two satellites of masses 3 M and M orbit the earth in circular orbits of radii r and 3 r respectively. The ratio of their speeds is

Question

Two satellites of masses 3 M and M orbit the earth in circular orbits of radii r and 3 r respectively. The ratio of their speeds is (A) 1: 1 (B)  √3 : 1 (C) 3: 1 (D) 9: 1

Tardigrade Admin · Accepted Answer

Orbital velocity v=√(G M/r). where, M = mass of the planet r= radius of the orbit Orbital velocity is independent of the mass of the orbiting body and is always along the tangent of the orbit. For a given planet (here earth), greater the radius of orbital, lesser will be the orbital velocity of the satellite (v propto (1/√r)) ∴ (v1/v2)=√(r2/r1)=√(3/1)

Q. Two satellites of masses $3 M$ and $M$ orbit the earth in circular orbits of radii $r$ and $3 r$ respectively. The ratio of their speeds is

$1 : 1$

$3$ : 1

$3 : 1$

$9 : 1$

Q. Two satellites of masses 3M and M orbit the earth in circular orbits of radii r and 3r respectively. The ratio of their speeds is

1:1

3​ : 1

3:1

9:1

Q. Two satellites of masses $3 M$ and $M$ orbit the earth in circular orbits of radii $r$ and $3 r$ respectively. The ratio of their speeds is

$1 : 1$

$3$ : 1

$3 : 1$

$9 : 1$