Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

Two satellites of Earth, $S_1$ and $S_2$ , are moving in the same orbit. The mass of $S_1$ is four times the mass of $S_2$ . Which one of the following statements is true?

The time period of $S_1$ is four times that of $S_2$ .

The potential energies of the earth and satellite in the two cases are equal.

$S_1$ and $S_2$ are moving at the same speed.

The kinetic energies of the two satellites are equal.

Step-by-Step Solution

Orbital Speed: The orbital speed of a satellite orbiting the Earth is given by $v = \sqrt{\frac{GM_E}{r}}$ , where $M_E$ is the mass of the Earth and $r$ is the orbital radius [Eq. 7.36]. This expression is independent of the mass of the satellite ( $m$ ). Since both satellites are in the same orbit (same $r$ ), they move at the same speed.
Time Period: The time period is given by $T^2 = \frac{4\pi^2 r^3}{GM_E}$ [Eq. 7.38]. This is also independent of the satellite's mass. Thus, their time periods are equal.
Potential Energy: Potential energy is $V = -\frac{GM_E m}{r}$ [Eq. 7.41]. It is directly proportional to the mass of the satellite ( $m$ ). Since $m_1 = 4m_2$ , the potential energy of $S_1$ is four times that of $S_2$ .
Kinetic Energy: Kinetic energy is $K = \frac{GM_E m}{2r}$ [Eq. 7.40]. It is also directly proportional to the mass $m$ . Thus, the kinetic energy of $S_1$ is four times that of $S_2$ .

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