Question

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.

Solution

Correct option is

 

Suppose, the mass of the particle is m. The gravitational potential energies of the particle at the earth’s surface and at a distance 0.5 Re from the earth’s surface are  

          

Hence gain in P.E. is   

        

This gain will come from the initial K.E.  of the particle, where v is the velocity of projection of the particle.

          

SIMILAR QUESTIONS

Q1

Determine the speed with which the earth would have to rotate on its axis so that a person on the equator would weigh 3/5 th as much as at present. Take the equatorial radius as 6400 km.

Q2

At what height above the earth’s surface the acceleration due to gravity will be 1/9 th of its value at the earth’s surface? Radius of earth is 6400 km.

Q3

The radius of the earth is approximately 6000 km. What will be your weight at 6000 km above the surface of the earth? At 12000 km above? At 18000 km above?

Q4

Calculate the gravitational field strength and the gravitational potential at the surface of the moon. The mass of the moon is  kg and its radius is 

Q5

The intensity of gravitational field at a point situated at earth’s surface is 2.5 N/kg. Calculate the gravitational potential at that point. Given: radius of earth, 

Q6

At a point above the surface of the earth, the gravitational potential is  and the acceleration due to gravity is 6.4 ms–2. Assuming the mean radius of the earth to be 6400 km, calculate the height of this point above the earth’s surface.   

Q7

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? 

Q8

 

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?

Q9

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  

Q10

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