SSC
The escape velocity on the surface of the Earth is approximately:
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Answer: Option C — 11.2 km/s
Detailed Solution
Escape velocity is the minimum speed that an object must be given, at the surface of a planet or other celestial body, to escape completely from its gravitational pull and never return, ignoring air resistance. For the Earth, it is about 11.2 kilometres per second, or about 40,000 kilometres per hour.
The formula for escape velocity is: ve = √(2GM/R) = √(2gR), where G is the universal gravitational constant, M is the mass of the planet, R is its radius and g is the acceleration due to gravity at its surface. This shows that:
Escape velocity depends on the mass and radius of the planet.
It does not depend on the mass of the object being launched; a tennis ball and a rocket need the same escape velocity.
It does not depend on the direction of launch (if air resistance is ignored).
Escape velocities of some bodies:
Moon: about 2.4 km/s. Because this is low, the Moon cannot hold an atmosphere; gas molecules easily escape.
Mars: about 5.0 km/s.
Jupiter: about 59.5 km/s, the highest among planets of the solar system.
Sun: about 618 km/s.
A body whose escape velocity exceeds the speed of light (about 3 lakh km/s) is a black hole; not even light can escape from it.
Escape velocity is related to orbital velocity. The orbital velocity needed to circle the Earth just above its surface is about 7.9 km/s. Escape velocity is √2 (about 1.414) times the orbital velocity near the surface. Rockets that send spacecraft to the Moon or Mars, such as Chandrayaan and Mangalyaan, must reach close to escape velocity.
Why not the other options?
- ✗7.9 km/s is the orbital velocity near the Earth's surface.
- ✗2.4 km/s is the escape velocity of the Moon.
- ✗42.1 km/s is roughly the speed needed to escape the solar system from the Earth's orbit.
Quick tip
Remember: Earth's escape velocity = 11.2 km/s (orbital velocity 7.9 km/s; escape = √2 × orbital); Moon = 2.4 km/s; Jupiter = highest among planets.
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Gravitation — Preparation
This question tests your understanding of Gravitation, a key topic in the General Knowledge section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
This topic covers Newton's law of universal gravitation, the acceleration due to gravity and how it varies, mass and weight, escape velocity, orbital velocity, satellites, Kepler's laws and weightlessness. Common questions ask how the value of g changes with height, depth and latitude (it is greatest at the poles and zero at the centre of the Earth), the Earth's escape velocity (about 11.2 km/s), and why astronauts feel weightless. Remember that mass stays the same everywhere, while weight changes with gravity. Practise the gravitation questions below, written in the style of the general awareness sections of exams such as SSC, banking, railways, CUET GAT, MAH CET and CLAT. Each question comes with a detailed explanation that adds related facts, so every question helps you revise more than one point.