A satellite A of mass m is at a distance of r from the surface of the earth. Another satellite B of mass 2m is at a distance of 2r from the earth's centre. Their time periods are in the ratio of

Question

A satellite A of mass m is at a distance of r from the surface of the earth. Another satellite B of mass 2m is at a distance of 2r from the earth's centre. Their time periods are in the ratio of (A) 1: 2 (B) 1: 16 (C) 1: 32 (D) 1: 2 √ 2

Tardigrade Admin · Accepted Answer

Time period does not depend on the mass. As T2 propto r3. (TA/TB)=(r3 / 2/23 / 2 r3 / 2)=1: 2 √2

Q. A satellite $A$ of mass $m$ is at a distance of r from the surface of the earth. Another satellite $B$ of mass $2 m$ is at a distance of $2 r$ from the earth's centre. Their time periods are in the ratio of

$1 : 2$

$1 : 16$

$1 : 32$

$1 : 22$

Time period does not depend on the mass.
As $T^{2} \propto r^{3}$ .
$\frac{T _{A}}{T _{B}} = \frac{r ^{3/2}}{2 ^{3/2} r ^{3/2}} = 1 : 22$

Q. A satellite A of mass m is at a distance of r from the surface of the earth. Another satellite B of mass 2m is at a distance of 2r from the earth's centre. Their time periods are in the ratio of

1:2

1:16

1:32

1:22​