Question

 

If the period of revolution of an artificial satellite just above the earth be Tand the density of earth be then prove that ρT2 is a universal constant. Also calculate the value of this constant. 

Solution

Correct option is

 

If the period of revolution of a satellite about the earth be T. then

                            

Where h is the height of the satellite from earth’s surface.

                        

The satellite is revolving just above the earth, hence h is negligible compared to Re.

                       

 where ρ is the density of the earth. Thus

                         

                        

Which is a universal constant. To determine its value,

          

SIMILAR QUESTIONS

Q1

The mass of the earth is  and its radius is  m. How much work will be done in taking a 10-kg body from the surface of the earth to infinity? What will be the gravitational potential energy of the body on the earth’s surface? If this body falls from infinity to the earth, what will be its velocity when striking the earth? 

Q2

 

The radius of earth is 6400 km and mass is  kg. What will be the gravitational potential energy of a body of 200 kg placed at a height of 600 km from the surface of the earth?

Q3

A body of mass m is moved from the surface of the earth to a height (his not negligible in comparison to radius of earth Re). Prove that the increase in potential energy is  

Q4

Calculate the velocity of projection of a particle so that the maximum height attained by the particle is 0.5 Re, where Re is radius of earth. The mass of earth is Me.

Q5

A satellite is revolving in a circular orbit at a distance of 2620 km from the surface of the earth. Calculate the orbital velocity and the period of revolution of the satellite. Radius of the earth = 6380 km, mass of the earth =  Nmkg–2 

Q6

A satellite is revolving in a circular orbit at a distance of 3400 km. calculate the orbital velocity and the period of revolution of the satellite. Radius of the earth = 6400 km and g = 9.8 ms –2.

Q7

 

(i) A satellite is revolving in an orbit close to the earth’s surface. Taking the radius of the earth as  find the value of the orbital speed and the period of revolution of the satellite.   

(ii) What is the relationship of this orbital speed to the velocity required to send a body from the earth’s surface into space, never to return?

Q8

 

An artificial satellite revolving coplanar with the equator around the earth, appears stationary to an observer on the earth. Calculate the height of the satellite above the earth.

Q9

 

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: 

Q10

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/s2).