Satellite motion - time period and energy — NEET & JEE Questions

Question 1 · difficulty L1 · recall

The time period of a satellite in a circular orbit of radius r around mass M is

• A. $T=2\pi\sqrt{\dfrac{r^3}{GM}}$
• B. $T=2\pi\sqrt{\dfrac{GM}{r^3}}$
• C. $T=\dfrac{GM}{r^2}$
• D. $T=2\pi rGM$

Question 2 · difficulty L2 · understanding

For circular satellite motion around the same planet, orbital period varies as

• A. $r^{3/2}$
• B. $r$
• C. $1/r$
• D. $r^2$

Question 3 · difficulty L2 · understanding

The total mechanical energy of a satellite of mass m in a circular orbit of radius r is

• A. $-\dfrac{GMm}{2r}$
• B. $+\dfrac{GMm}{2r}$
• C. $-\dfrac{GMm}{r}$
• D. $0$

Question 4 · difficulty L2 · understanding

For a bound satellite orbit, the total mechanical energy is

• A. negative
• B. positive
• C. always zero
• D. undefined

Question 5 · difficulty L3 · application

If the orbital radius of a satellite doubles around the same planet, its period changes by a factor of

• A. $2\sqrt2$
• B. 2
• C. 4
• D. $\sqrt2$

Question 6 · difficulty L3 · application

A satellite in a circular orbit has kinetic energy K. What is the magnitude of its gravitational potential energy?

• A. 2K
• B. K
• C. K/2
• D. 4K

Question 7 · difficulty L3 · application

A satellite in a circular orbit has total energy E. Which relation is correct if K is kinetic energy?

• A. $E=-K$
• B. $E=K$
• C. $E=-2K$
• D. $E=2K$

Question 8 · difficulty L3 · application

A satellite is moved from a lower circular orbit to a higher circular orbit. Its total mechanical energy

• A. increases, becoming less negative
• B. decreases, becoming more negative
• C. remains unchanged
• D. becomes zero immediately

Question 9 · difficulty L4 · application

If a satellite's circular orbital radius becomes four times larger, its period becomes

• A. 8 times
• B. 4 times
• C. 2 times
• D. 16 times

Question 10 · difficulty L4 · application

A satellite of mass m orbits at radius r with total energy $-E_0$. If the orbital radius becomes 2r, the new total energy is

• A. $-E_0/2$
• B. $-2E_0$
• C. $+E_0/2$
• D. $-E_0$