NEET Practice Questions (MCQs) with Answers & Solutions

The period (T) of a satellite in a circular orbit is given by $T = 2rac{ ext{ extpi}}{ u}$ where $ u$ is the orbital velocity. Using the relationship for orbital velocity $ u = rac{GM}{r}$, we derive $T = 2 ext{ extpi}rac{r^{3/2}}{ ext{ extpi}rac{GM}{r}}$. Here, the period of the satellite depends on the radius of the orbit and the mass of the planet, but not on the mass of the satellite. Therefore, the period of the satellite is independent of the mass of the satellite.

$ \upsilon = \sqrt { GM \over R } \Rightarrow { V_A \over V_B} = \sqrt { R_E \over R_A } = \sqrt { R \over 4R } = { 1 \over 2 } $ $ \therefore { V_A \over V_B } = {3V \over VA } $ $ V_E = 6V $

The orbital velocity of a satellite near Earth's surface can be calculated using $ u = rac{GM}{r}$, where G is the gravitational constant, M is the mass of the Earth, and r is the radius of the Earth. For Earth, this velocity is approximately 8 km/s. Therefore, the correct option is 8 km/s.

The speed of a satellite in an elliptical orbit is greatest when it is closest to the Earth due to the conservation of angular momentum. This point is known as the perigee. In an elliptical orbit, the gravitational force does more work on the satellite as it moves closer to the Earth, increasing its speed.

If the height of the satellite is negligible compared to the radius of the Earth, the orbital velocity 'v' is given by the formula: \[ v = \\sqrt{gR} \] where 'g' is the acceleration due to gravity and 'R' is the radius of the Earth.

$ \upsilon \alpha {1 \over \sqrt r } $ % increase in speed = 1\2 % decrease in radius = 1/2 (1%) = 0.5 %

$ \upsilon = \sqrt { GM \over r } $

The orbital velocity of a satellite does not depend on its mass. It depends only on the mass of the Earth and the radius of the orbit. Hence, the statement 'The orbital velocity depends on the mass of the satellite' is incorrect.

The weight of an astronaut in an artificial satellite revolving around the Earth is zero. This is because the astronaut and the satellite are both in free fall towards the Earth, creating a condition of apparent weightlessness. The gravitational force provides the centripetal force needed to keep the satellite in orbit, but since the astronaut is also in free fall, they do not experience this force as weight.

6R from the surface of earth and 7R from the center