Question

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? 

Solution

Correct option is

 

The work done in taking a body of mass m from the surface of the earth to infinite is 

                                      

Where Me is the mass of the earth and Re its radius. Putting the values:  

    

The gravitational potential energy at the earth’s surface is

    

The work done in taking the body from the earth to infinity will be obtained in the form of kinetic energy when the body falls back on the earth. Hence if the body strikes the earth with a velocity v, then

                  

  

                   

SIMILAR QUESTIONS

Q1

The weight of a person on the earth is 80 kg. What will be his weight on the moon? Mass of the moon = 7.34 × 1022kg, radius = 1.75 × 106 m and gravitational constant G = 6.67 × 10 –11 Nm2/kg2. What will be the mass of the person at the moon? If this person can jump 2 meter high on the earth, how much high can he jump at the moon? If he can walk 100 m in 1 minute on the earth, then how much will he walk in 1 minute on the moon?

Q2

What will be the acceleration due to gravity on the surface of the moon if its radius is 1/4th the radius of the earth and its mass is (1/80)th the mass of the earth. 

Q3

 

Calculate that imaginary angular velocity of the earth for which effective acceleration due to gravity at the equator becomes zero. In this condition what will be the length (in hours) of the day?

(Re = 6400 km, g = 10 ms–2)

Q4

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.

Q5

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.

Q6

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?

Q7

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 

Q8

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, 

Q9

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.   

Q10

 

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?