Physics · Gravitation · NEET
No. Orbital velocity is the speed to go around Earth in a circle near the surface, about 7.9 km/s. Escape velocity is the speed to leave Earth forever, about 11.2 km/s. The link is v_e = sqrt(2) x v_orbital, so escape velocity is about 1.414 times the orbital velocity. NEET often mixes these two, so keep both numbers ready: 7.9 to orbit, 11.2 to escape.
No. From v_e = sqrt(2GM/R) = sqrt(2gR), only Earth's mass M and radius R appear, not the object's mass m. A cricket ball and a satellite both need the same 11.2 km/s. The mass m cancels out because both kinetic energy and gravitational PE contain m. This is a very common NEET trap.
Put the numbers into v_e = sqrt(2gR): g = 9.8 m/s^2 and R = 6.4x10^6 m. So v_e = sqrt(2 x 9.8 x 6.4x10^6) = sqrt(1.254x10^8) = 1.12x10^4 m/s = 11.2 km/s. That is why the value is fixed for Earth's surface — it comes straight from g and R.
No, the magnitude 11.2 km/s is the same in every direction (ignoring air and Earth's rotation). Escape velocity is really an escape speed. The energy equation uses only the size of the velocity, not its direction, because gravitational PE depends only on distance r, not on angle. That is why NCERT calls it 'escape speed'.
If speed is less than 11.2 km/s, the body rises, stops, and falls back to Earth. If it is exactly 11.2 km/s, it just barely reaches infinity with zero speed left. If it is more than 11.2 km/s, it escapes and still has leftover speed at infinity, found from v_infinity = sqrt(u^2 - v_e^2).
Try the real previous-year questions from this chapter — each with the answer and a full solution.
About 11.2 km/s, which equals 11,200 m/s. It comes from v_e = sqrt(2gR) with g = 9.8 m/s^2 and R = 6.4x10^6 m.
v_e = sqrt(2GM/R), which also equals sqrt(2gR) at the surface, since g = GM/R^2. For Earth this gives 11.2 km/s.
Physically it is a speed (scalar). Its value is the same in all directions, which is why NCERT prefers the name escape speed.
v_e = sqrt(2) x v_orbital. So escape velocity (11.2 km/s) is about 1.414 times the orbital velocity near the surface (7.9 km/s).
The Moon has smaller g and smaller radius R, so v_e = sqrt(2gR) is smaller — about 2.4 km/s. That is why gases escaped and the Moon has almost no atmosphere.
