Escape velocity and orbital velocity — NEET & JEE Questions

Question 1 · difficulty L1 · recall

The escape speed from the surface of a spherical planet of mass $M$ and radius $R$ is

• A. $\sqrt{\dfrac{2GM}{R}}$
• B. $\sqrt{\dfrac{GM}{R}}$
• C. $\dfrac{GM}{R^2}$
• D. $\dfrac{2GM}{R}$

Question 2 · difficulty L2 · understanding

The circular orbital speed just above a planet's surface is

• A. $\sqrt{\dfrac{GM}{R}}$
• B. $\sqrt{\dfrac{2GM}{R}}$
• C. $\dfrac{GM}{R^2}$
• D. $2\pi R$

Question 3 · difficulty L2 · understanding

For the same planet and same radius, escape speed and circular orbital speed are related by

• A. $v_e=\sqrt2\,v_o$
• B. $v_e=v_o$
• C. $v_e=2v_o$
• D. $v_e=v_o/\sqrt2$

Question 4 · difficulty L2 · understanding

Escape speed from a planet is independent of the mass of the escaping object because

• A. the object's mass cancels in the energy equation
• B. gravity does not act on massive objects
• C. all objects have zero gravitational potential energy
• D. only volume matters

Question 5 · difficulty L3 · application

A planet has surface orbital speed $8\,\text{km s}^{-1}$. What is its surface escape speed approximately?

• A. 5.7 km/s
• B. 8 km/s
• C. 11.3 km/s
• D. 16 km/s

Question 6 · difficulty L3 · application

If the mass of a planet is doubled while its radius remains the same, its escape speed changes by a factor of

• A. $1/2$
• B. $1/\sqrt2$
• C. $\sqrt2$
• D. 2

Question 7 · difficulty L3 · application

If the orbital radius of a satellite in a circular orbit is increased by a factor of 4 around the same planet, its orbital speed becomes

• A. 4 times
• B. 2 times
• C. half
• D. one-fourth

Question 8 · difficulty L3 · application

A planet has the same mass as Earth but twice Earth's radius. Compared with Earth's escape speed, its escape speed is

• A. twice
• B. $\sqrt2$ times
• C. $1/\sqrt2$ times
• D. half

Question 9 · difficulty L4 · application

A satellite moves in a circular orbit of radius $r$ around a planet. If the planet's mass becomes four times larger but the orbital radius is unchanged, the orbital speed becomes

• A. unchanged
• B. twice
• C. four times
• D. half

Question 10 · difficulty L4 · application

At a distance $r$ from a planet's centre, the local escape speed is $v_e$. What is the circular orbital speed at the same radius?

• A. $v_e/\sqrt2$
• B. $v_e/2$
• C. $\sqrt2v_e$
• D. $2v_e$