Does the escape speed of a body from the earth depend on

(a) the mass of the body,

(b) the location from where it is projected,

(c) the direction of projection,

(d) the height of the location from where the body is launched?

Asked by Pragya Singh | 1 year ago |  63

##### Solution :-

The escape speed is given by the expression

$$v= \sqrt{\dfrac{2GM}{R}}=\sqrt{2gR}$$

(a) The escape speed of a body from the Earth does not depend on the mass of the body.

(b) The escape speed of a body from the Earth does not depend on the location from where a body is projected.

(c) The escape speed does not depend on the direction of projection of a body.

(d) The escape speed of a body depends upon the height of the location from where the body is launched since the escape velocity depends on the gravitational potential at the point from which it is launched. This potential in turn depends on the height.

Answered by Abhisek | 1 year ago

### Related Questions

#### A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km s–1.

A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km s–1. If 20% of its initial energy is lost due to martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it? Mass of mars = 6.4×1023 kg; radius of mars = 3395 km; G = 6.67×10-11 N m2 kg–2.

#### A spaceship is stationed on Mars. How much energy must be expended on the spaceship

A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system? Mass of the space ship = 1000 kg; mass of the sun = 2×1030 kg; mass of mars = 6.4×1023 kg; radius of mars = 3395 km; radius of the orbit of mars = 2.28 ×108 km; G = 6.67×10-11 N m2kg–2.

#### A star 2.5 times the mass of the sun and collapsed to a size of 12 km rotates with a speed

A star 2.5 times the mass of the sun and collapsed to a size of 12 km rotates with a speed of 1.2 rev. per second. (Extremely compact stars of this kind are known as neutron stars. Certain stellar objects called pulsars belong to this category). Will an object placed on its equator remain stuck to its surface due to gravity? (mass of the sun = 2×1030 kg).