Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, TA/TB, is:

Question

Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, TA/TB, is: (A) 2 (B) √(1/2) (C) 1 (D) (1/2)

Tardigrade Admin · Accepted Answer

Orbital velocity V = √(GMe/r) TA = (1/2) mA VA2 TB = (1/2)mB VB2 ⇒ (TA/TB) = (m × (Gm/R)/2m × (Gm)2R) ⇒ (TA/TB) = 1

Q. Two satellites, $A$ and $B$ , have masses $m$ and $2 m$ respectively. A is in a circular orbit of radius $R$ , and $B$ is in a circular orbit of radius $2 R$ around the earth. The ratio of their kinetic energies, $T_{A} / T_{B}$ , is:

$2$

$\frac{1}{2}$

$1$

$\frac{1}{2}$

Orbital velocity $V = \frac{GM e}{r}$
$T_{A} = \frac{1}{2} m_{A} V_{A}^{2}$
$T_{B} = \frac{1}{2} m_{B} V_{B}^{2}$
$\Rightarrow \frac{T _{A}}{T _{B}} = \frac{m \times \frac{G m}{R}}{2 m \times \frac{G m}{2 R}}$
$\Rightarrow \frac{T _{A}}{T _{B}} = 1$

Q. Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, TA​/TB​, is:

2

21​​

1

21​

Orbital velocity V=rGMe​​ TA​=21​mA​VA2​ TB​=21​mB​VB2​ ⇒TB​TA​​=2m×2RGm​m×RGm​​ ⇒TB​TA​​=1

Q. Two satellites, $A$ and $B$ , have masses $m$ and $2 m$ respectively. A is in a circular orbit of radius $R$ , and $B$ is in a circular orbit of radius $2 R$ around the earth. The ratio of their kinetic energies, $T_{A} / T_{B}$ , is:

$2$

$\frac{1}{2}$

$1$

$\frac{1}{2}$

Orbital velocity $V = \frac{GM e}{r}$
$T_{A} = \frac{1}{2} m_{A} V_{A}^{2}$
$T_{B} = \frac{1}{2} m_{B} V_{B}^{2}$
$\Rightarrow \frac{T _{A}}{T _{B}} = \frac{m \times \frac{G m}{R}}{2 m \times \frac{G m}{2 R}}$
$\Rightarrow \frac{T _{A}}{T _{B}} = 1$