## Question

A mass of is to be compressed in the form of a sphere. The escape velocity from its surface is What should be the radius of the sphere. Gravitational constant

### Solution

89 m

Let *M* be the mass of the sphere and *R* its radius. The escape velocity from the surface of the sphere is given by

Substituting the given values:

#### SIMILAR QUESTIONS

An artificial satellite is revolving at a height of 500 km above the earth’s surface in a circular orbit, completing one revolution in 98 minutes. Calculate the mass of the earth. Given:

If the period of revolution of an artificial satellite just above the earth be *T*and the density of earth be then prove that ρT^{2} is a universal constant. Also calculate the value of this constant.

A space-craft is launched in a circular orbit near the earth. How much more velocity will be given to the space-craft so that it will go beyond the attraction force of the earth. (Radius of the earth = 6400 km, *g* = 9.8 m/s^{2}).

An artificial satellite of mass 200 kg revolves around the earth in an orbit of average radius 6670 km. Calculate its orbital kinetic energy, the gravitational potential energy and the total energy in the orbital.

(Mass of earth = 6.0 × 10^{24} kg, *G* = 6.67 × 10^{–11} Nm^{2} kg^{ –2}).

With what velocity must a body be thrown upward from the surface of the earth so that it reaches a height of 10 *R _{e}*? Earth’s mass and

*G*= 6.67 × 10

^{ –11}Nm

^{2}kg

^{–2}.

A rocket is launched vertically from the surface of the earth with an initial velocity of 10 km s^{–1}. How far above the surface of the earth would it go? Mass of the earth = 6.0 ×^{ }10^{24} kg, radius = 6400 km and *G* = 6.67 ×^{ }10^{ –11} Nm^{2} kg^{ –2}. ^{ }

The escape velocity of a body from earth is 11.2 km s^{–1}. If the radius of a planet be half the radius of the earth and its mass be one-fourth that of earth, then what will be the escape velocity from the planet?

A body is at a height equal to the radius of the earth from the surface of the earth. With what velocity be it thrown so that it goes out of the gravitational field of the earth? Given:

N m^{2} kg^{–2}.

A particle falls on the surface of the earth from infinity. If the initial velocity of the particle is zero and friction due to air is negligible, find the velocity of the particle when it reaches the surface of the earth. Also find its kinetic energy. (Radius of earth is 6400 km and *g* is 9.8 m/s^{2}.)

Imagine a planet whose diameter and mass are both one-half of those of earth. The day’s surface temperature of this planet reaches upto 800 K. Are oxygen molecules possible in the atmosphere of this planet? Give calculation. (Escape velocity on earth’s surface = 11.2 km s^{–1}, Boltzmann’s constant

*k* = 1.38 × 10^{–23} JK^{–1}, mass of oxygen molecule = 5.3 × 10^{–26 }kg.)