Question

The escape speed of a body from the earth regarded as a uniform (non-rotating) sphere depends on :

• A. The mass of the body
• B. The direction of projection
• C. The location of the projection on the earth's surface
• D. The height of location from the earth's surface from where the body is launched

Answer 1

The correct option is D The height of location from the earth's surface from where the body is launched

Answer is D.
The escape velocity is given as $V=\sqrt{\frac{2GM}{R}}$.
The escape velocity is independent of the mass of the body. The escape velocity depends on the gravitational potential at the point of projection. As the potential depends to a minor extent, on the altitude and height of the point, the location affects it to a minor extent.
The escape velocity is independent of the direction of projection.
The escape velocity depends on the height of the location. For a projection point at a height h from the ground level, $V=\sqrt{\frac{2GM}{R+h}}$.
Hence, it depends in the height of projection point.